Your trying to measure WOW. A strobe test will tell you speed only..
Blow all the dust and crap out of the motor first.
Remove the belt and spin the platter. If you see the platter come to an abrupt halt after a spin you found your problem. If not it’s the motor and it need to be lubed and cleaned. Make sure the bushings are not wore out and the armature is making contact with the field coils or to much end play. It’s only one or the other. The motor or the spindle. If the spindle well is full of crap, clean it out service the shaft and change the oil. It should spin for 100 years when it’s clean AND burr free.
OH WOW, NO WOW... Boo Boo.
Just a guess though.. :-)