How can I (masters in mathematics) prepare for an admission for PhD in economics? I finished my master’s in mathematics a year ago from ETH Zurich.  Now I want to do a PhD in economics, preferably at a top graduate school. My questions are: 


Would admission committee give minus points for me if I have a gap for two years at the time of PhD application? I want to apply in the US in December 2020, and it would be two years of my masters completion by then. I will be teaching mathematics at undergraduate level during these two years. 
How can I prepare myself for an admission into a top PhD program for economics? Would getting involved in a research project in economics with a local economist be seen an advantage for me? Would working at a local research institute be helpful? How can I make my application competitive? How can I exhibit the knowledge in economics that the top PhD programs demand? 


The last time I studied economics was during my high school, where I did two basic courses on micro- and macro-economics.
I'd consider mathematics as an excellent footing for economics, perhaps top graduate schools and their professors will agree, ask them.

I don't see that delaying your application to teach mathematics for two years will help, and I don't think that delaying to "[get] involved in a research project in economics with a local economist" or "working at a local research institute" will provide a significant advantage. But, top graduate schools and their professors may disagree. Again, ask them.

It seems you don't know whether executing your plan (or aspects of your plan) will help make your application more competitive. This makes your question rather personal (indeed, you've gotten at least one close vote - not mine - on this basis). I strongly recommend asking the institutes involved, the relevant professors, or a combination of both, they can guide you, the broader Internet cannot.