For the actual post: especially in the body on frame cars of japanese origin, the motor mount Spacers were made of soft squishy rubber that all came from the same supplier. These are not like the indestructible urethane aftermarket type. After lots of hard revving or even just years of weather exposure (high heat, road salt, etc) they break down like wiper blades.
With that in mind, its easy to test. With the engine off, go push on it side to side and see how much wiggle you get. With the engine on, leave it in park (of course) and blip the throttle body through short rev ranges. Bet it moves a lot if your mounts are trashed! As the rpm's climb, the engine movement settles down as all the torque presses the engine down on the mounts.
I drove a '90 240sx for years with this same issue and didn't notice a problem mechanically til I swapped the transmission. It'd shake and shimmy at stoplights like it had a blown hemi under the hood, resulting in the occasional 'seat wood'. (TMI!!) though the lady passenger of the time didn't seem to mind.
Now if your motor vibrates when doing highway speed like something is about to explode under there (ie under load), that sounds quite a bit more complicated, and in which case, you will soon see money flowing down the street behind you in the form of engine internals becoming externals...