Lift the front wheel offa the ground. Disconnect the cable from the speedo. Turn the front wheel by hand, observe the inner cable. If it is turning, the speedo has quit. If it is not turning, remove the cable from the front wheel. The cable should pull out from one end. If the cable is complete, as in one piece and turns freely in the outer tube, then it is likely the piece in the wheel housing that is the problem. Also my prime suspect, just because. Remove the front wheel and study the bits that are supposed to be turning. There is a flat washer with two tangs at a 90 degree angel that connect to other bits. When removing make note of the order of bits.
The 1996 Royal Star has an electronic speed sensor on the rear final drive. High Tech for that year model.
It has probably failed. Part number 4NK-83755-00-00. You might be lucky and find the internal "pick up" just needs to be cleaned.
Check ALL wiring before you buy a replacement. The sensor ain't cheap.
The other possibility would be the speedo itself. You do not want that to be the problem $$$ ! (The sensor is most likely).
97 Yamaha royal star 44k miles. Decent shape bought used. I feel like it has to be an electrical issue just not sure where to start . Battery cables tight at battery. Don’t see it smell any oblivious burnt wires
If it is the same as mine it is all digital. Either way the place to look for help is the Royal Star / Venture forums. Can't post a link here but google is your friend. Some very knowledgeable people there.