user72815: I had some bitcoin on Electrum and some on Coinbase before the October fork. I assume I won't be able to claim Bitcoin gold for the amount that was on Coinbase. 
Since the fork, I've moved all my Bitcoin to a Ledger Nano S. When I try to use their Split Tool, it doesn't show a balance. I've seen a number of how-tos that entail using a Coinomi which only works on an Android device (of which I do not own). 
So my question it, how do I obtain my Bitcoin Gold now that my Bitcoin is on my Ledger Nano S?

user65907: Regarding Coinbase, they do not support Bitcoin Gold right now, but there is a possibility they will in the future.
The Nano Ledger split procedure is for if you had Bitcoin in their wallet during the fork.
You can't use it to claim Bitcoin Gold from an external private key.
So for the time being you can't claim Bitcoin Gold with your Ledger Nano.
However, you can use one of the wallets listed under Bitcoin Gold official webpage if you trust them.
Honestly, I wouldn't trust all the wallets they endorse since after the two major incidents that happened a while ago. 
Incident 1 - One of the wallet provider they endorsed turned out to be malicious.
Incident 2 - Their official wallet got compromised.
As of now I only deem Coinomi, Ledger and Trezor as the trustworthy wallets for BTG.

user4276: Your BTG is still "in" your Electrum wallet
Moving your BTC from Electrum to Ledger after the fork has not done anything to your BTG. Your BTG all remains on the addresses that correspond to the private keys in your Electrum wallet. Whatever has been generated or transferred to your Ledger is irrelevant and has not affected the BTG. 
The nature of a hard fork is that everything up to the fork is exactly duplicated. If your BTC was in your Electrum wallet at the time of the fork, then all those addresses, their balances, and corresponding private keys are exactly duplicated on the BTG fork. Anything done after the fork affects only that fork. Moving your BTC to ledger after the fork does nothing to the duplicated BTG. And moving your BTG after the fork does nothing to the BTC. 
The Ledger split feature is showing a zero BTG balance because all you BTG remains still in the addresses in your Electrum wallet. You need the private keys from your Electrum wallet to claim your BTG. If you wanted to use Ledger's split feature, you should have transferred all your BTC to Ledger before the fork. 
Use Coinomi with an android emulator
You mention you don't want to use Coinomi because it's an android only wallet. I understand your reservation and so do many others. That's why there's many Coinomi setup guides that include running the app via BlueStacks, an android emulator. There's a free version that works just fine for me. 
Once you install BlueStacks and Coinomi you will need to export the BTC private keys from electrum and sweep them into a BTG wallet in Coinomi. Use this answer to help you further.
Your Coinbase BTG balance is unretrievable.
Regarding your pre-fork Coinbase balance, you are at Coinbase's mercy. Unless they decide to support BTG, you will never be able to retrieve it. This lack of full control and ignorance of private keys is a major downside of some hosted wallets, Coinbase included. 

72815: <p>I had some bitcoin on Electrum and some on Coinbase before the October fork. I assume I won't be able to claim Bitcoin gold for the amount that was on Coinbase. </p>

<p>Since the fork, I've moved all my Bitcoin to a Ledger Nano S. When I try to use their Split Tool, it doesn't show a balance. I've seen a number of how-tos that entail using a Coinomi which only works on an Android device (of which I do not own). </p>

<p>So my question it, how do I obtain my Bitcoin Gold now that my Bitcoin is on my Ledger Nano S?</p>
 65907: <p>Regarding Coinbase, <a href="https://support.coinbase.com/customer/portal/articles/2892196-bitcoin-gold-faq" rel="nofollow noreferrer">they do not support Bitcoin Gold right now, but there is a possibility they will in the future</a>.</p>

<p>The Nano Ledger split procedure is for if you had Bitcoin in their wallet during the fork.<br>
You can't use it to claim Bitcoin Gold from an external private key.<br>
So for the time being you can't claim Bitcoin Gold with your Ledger Nano.</p>

<p>However, you can use one of the wallets listed under <a href="https://bitcoingold.org/downloads/" rel="nofollow noreferrer">Bitcoin Gold official webpage</a> if you trust them.<br>
Honestly, I wouldn't trust all the wallets they endorse since after the two major incidents that happened a while ago. </p>

<p><a href="https://www.coindesk.com/bitcoin-gold-wallet-scam-nets-3-million-illicit-earnings/" rel="nofollow noreferrer">Incident 1</a> - One of the wallet provider they endorsed turned out to be malicious.<br>
<a href="https://bitcoingold.org/vulnerable-wallets/" rel="nofollow noreferrer">Incident 2</a> - Their official wallet got compromised.</p>

<p>As of now I only deem Coinomi, Ledger and Trezor as the trustworthy wallets for BTG.</p>
 4276: <h1>Your BTG is still "in" your Electrum wallet</h1>

<p>Moving your BTC from Electrum to Ledger <em>after the fork</em> has not done anything to your BTG. Your BTG all remains on the addresses that correspond to the private keys in your Electrum wallet. Whatever has been generated or transferred to your Ledger is irrelevant and has not affected the BTG. </p>

<p>The nature of a hard fork is that everything up to the fork is exactly duplicated. If your BTC was in your Electrum wallet at the time of the fork, then all those addresses, their balances, and corresponding private keys are exactly duplicated on the BTG fork. Anything done after the fork affects only that fork. Moving your BTC to ledger after the fork does nothing to the duplicated BTG. And moving your BTG after the fork does nothing to the BTC. </p>

<p>The Ledger split feature is showing a zero BTG balance because all you BTG remains still in the addresses in your Electrum wallet. You need the private keys from your Electrum wallet to claim your BTG. If you wanted to use Ledger's split feature, you should have transferred all your BTC to Ledger <em>before</em> the fork. </p>

<h1>Use Coinomi with an android emulator</h1>

<p>You mention you don't want to use Coinomi because it's an android only wallet. I understand your reservation and so do many others. That's why there's many Coinomi setup guides that include running the app via <a href="https://www.bluestacks.com" rel="nofollow noreferrer">BlueStacks, an android emulator.</a> There's a free version that works just fine for me. </p>

<p>Once you install BlueStacks and Coinomi you will need to export the BTC private keys from electrum and sweep them into a BTG wallet in Coinomi. <a href="https://bitcoin.stackexchange.com/questions/64691/can-i-sell-my-btc-and-still-claim-my-bch/64722#64722">Use this answer to help you further.</a></p>

<h1>Your Coinbase BTG balance is unretrievable.</h1>

<p>Regarding your pre-fork Coinbase balance, you are at Coinbase's mercy. Unless they decide to support BTG, you will never be able to retrieve it. This lack of full control and ignorance of private keys is a major downside of some hosted wallets, Coinbase included. </p>
