Neither Mindset nor Mindset II. Mindset II had the 640 x 400 four-color mode upgrade. Double-buffered but interlaced. Could be genlocked to another Mindset.
I wonder if there's some top-class Japanese x86 machines from the "IBM workalike" era.
A composite compatible output addon, called the TV/Game Adapter, was planned but never released for the Tandy 2000; if released it might not have supported genlocking or really much beyond getting 16-color 320x200 or so video onto a TV. Until recently the only graphical game I recall actually being released for the machine was a special version of Flight Simulator; but recently on Facebook I saw a photo of a 2000 running some sort of video poker or other card game. It was unlikely to have been very fast paced and may even have been written in GW-BASIC; I don't know much about it.