Refresh rate on TV is gonna be 50 or 60Hz depending on if you feed it PAL or NTSC signal and it will *always* have 15.625 or 15.750kHz line rate, which means the resolution is fixed (100/120Hz TVs run at double the line rate, but they still only accept SDTV input which they digitally frame double before outputting). Vast majority of the TVs are not multisync and especially not over composhit or S-video connection which is only able to transfer 240p/288p/480i/576i signal with only very mild deviations. Video card outputs are always 720 x 486i/576i on their TV out over composhit/S-video as per ITU BT.601 spec. vast majority of TVs will reject anything that isn't.
Bear in mind that TVs use much slower phosphors than computer monitors, because they must show interlaced broadcast content and to reduce flicker the phosphors have higher presistence.
A ghetty way is using a phone etc. to record the buzzing sound that comes from the TV and do a spectrogram on it, you will see the harmonics of the noise from deflection system. There should be a 50/60Hz peak with a number of harmonics and als, a 15.625/15.750kHz peak. To properly verify the frame rate you need an oscilloscope or perhaps a multimeter that can show frequency and measure the frame amplifier input and/or output inside the TV, but you can also measure the video signal directly (multimeter will not help with the video signal).