My rear tire will not move car has set for a year or so what do I do to fix this

could be from worn tie rod ends, suspension ball joints , worn suspension rubbers and failing shock absorbers
take it to an accredited suspension service center for a complete check including the rear end as the front floating sensation could be from a problem rear end suspension set up and shock absorbers
I am well aware that every tire shop says rotate tires but in reality you just move a problem tire from one corner to the other, fail to see a wear problem develop in the tires ( indicates alignment or tire case problem) and costs 4 tires at a time instead of 2 which is not really economical as well
consider this front drive cars wear out front tires at the rate of 3 to rear tires 1 and I think you get the picture (rear drive cars rear tires 2 to front 1) or if there is a case problem with a tire it is lost in the rotation process and becomes dangerous on the road

if it has independent rear suspension then have the suspension rubbers checked and replace if necessary. Next for all wheel alignments it is essential that the rear end is aligned first to stop this tyre wear before the front wheels are aligned . IF you have leaf springs at the rear check for axle alignment and broken centre bolts or worn rubbers at the centre bolt mounts.

Could be a tire or wheel problem even tho you have new tires.
If the tires were balanced on a machine, the machine spins the wheels at around 30 mph. That is good enough for most cars and most normal speeds.
You could move the front tires to the rear and see if the vibration moves to the seats.

Does the mustang have independent (IRS) axel or the solid 8.8 rear axel?

You didn't say anything about tires and wheels, have you rotated the tires to see if the problem moves to the front of the car ?
If the car is 20+ years old, the mounts for the transaxle could be worn enough to cause a vibration. And one of the axles/driveshaft could be bent.

You didn't mention if you ever rotated the tires. I suggest you get them re-balanced and put the fronts on the rear. I recommend putting them front to back without crossing them. There's been an argument about that for many years and I still believe that crossing will cause belts to shift inside the tire and that can cause it to fail if you reverse the rolling rotation, especially if no rotation has been done for a long time. (rotate about once a year) It may also be a good idea to replace your front shock absorbers. Unless you live somewhere it gets very hot, I'd also run your tire pressure at 35psi. If you normally run it lower, it may feel a bit hard at first but it's easy to get used to and the tires will last longer.

See if the tire is if good condition .How long have you use this tire,some when using it too long it loses it's shape,that why it make that noise,it loses the circular shape,this is one possibility,second possibility is you near two check the wheel bearing may be it need to be lubricate with grease.Hope that clear your mind and help you.

Could be tire noise, could be rear wheel bearing, differential (if rear wheel driven), or could be something associated with the brake.

Try swapping the tire with another tire. If the noise moves with the tire, it's the tire. If it stays, it's brakes (unlikely for the noise you mention), rear wheel bearing, or rear differential (lack of oil). Will probably need to have a mechanic to identify and repair.

cheap tires wear fast, make sure you keep the proper psi