Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Private; Flight Crew Multiengine
Flight Crew Last 90 Days 6; Flight Crew Total 2900; Flight Crew Type 50
Confusion
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Ground Incursion Taxiway
Flight Crew Requested ATC Assistance / Clarification
Environment - Non Weather Related; Human Factors; Airport
I was on a training flight with an instructor but was PIC.  The ATIS at ZZZ stated that markings were nonstandard.  We landed on Runway XX and I was instructed by the Tower to taxi to the end of the runway.  The airport was nearly empty with no flights going on.  I was instructed by the Tower to taxi straight then to taxiway to the FBO. I never saw any sign for taxiway.  There were no FBO signs and in the past I have been asked to taxi to the parking area.  I thought that the terminal must be where the FBO was so taxied straight ahead well out of the way of Aircraft Y that was stationary on a taxiway 90 degrees to our path. The Tower intended for me to turn left just after departing the runway toward the area that is usually full of airplanes and the opposite of the direction of the general aviation parking. The Controller apparently was trying to communicate both on the Tower and ground frequencies.  He never asked that I switch to ground which made sense with only 2 other planes on the entire airport.  I never heard the Aircraft Y make a call so assume that he was on ground.The area this occurred in is confusing with limited markings and I was requested to do something that was counterintuitive to the direction I had thought I would be going especially in light of the fact that in usual times when the airport is busy I had never been asked to go to the north after departing the runway due to the air tour planes. I failed to follow the taxi instructions that the Tower gave me but it would have been nice if the taxiway signs were better or if he had requested that I turn off one taxiway sooner to avoid any possible conflicts. Interestingly enough I would chalk this one up to the COVID times as if the airport were busy I think this would have been less likely as I would have been more on guard for any potential conflicts and likely listened more closely and asked for progressive taxi instructions if they were unclear to me.
Pilot reported confusing taxiway signs and instructions from ATC resulted in a taxiway incursion.