Technics 1200MKII Burning Smell

Next time it happens, pull the platter off and see (smell) if the odor is more obvious, or even if there's some smoke. At the same time, look for any obvious signs of something awry on the pc board.

Unfortunately, you can't leave the platter 'on' while doing the inspection, since it will harm the motor (there's a warning sticker under the mat) but if you move fast you may be able to detect the cause (resistor frying, etc.).

Cigarettes anyone? Since these things were the T-34 of the turntable world -a lot of 'em spent time in bars back in the smoke'em if ya got 'em days.Have serviced several that had been brilliantly cleaned up at some point - but still smelled like stale cigarettes after a few min. of playing.
FWIW - amps can be a bigger problem in terms of warm up odor.

check the power cord and plug...?

Your turntable may be long overdue for some motor spindle oil. It's supposed to be replenished after every 2000 to 3000 hours of play, and I bet the overwhelming majority of SL12x0 owners have never oiled their turntables. You can get a small tube (it'll last a lifetime) of the official oil from kabusa.com for $4.95.