Steering wheel shake/vibration while stopped/idle; steering wheel play.

What's up everyone

I wanted to get some input from ya'll after I searched the site and internet for something similar to what I'm running into. I recently bought an auto 97 Tacoma single cab with about 278k (2RZ) and have noticed that when idle/stopped the steering wheel often vibrates/shakes considerably. I've only noticed the shaking/vibration at a stop when idling and usually this starts when something like the AC kick in but will be intermittent as I am stopped and idling. Aside from the shaking/vibration at idle it does seem like the steering wheel has some slight play and I can hear a rattle coming from somewhere within the steering column from time to time. I will try and get a video uploaded shortly.

The culprits I'm suspecting are
1. Bad engine mounts
2. Something loose in steering column
3. Harmonic balancer out of circle

Appreciate any feedback !

 

Have you tried shifting into neutral while idling ........ does it still shake??

 

If you up the rev’s while it’s shaking, does the vibration go away?

 

Steering wheel still vibrates even when shifting into neutral. Shaking/vibration goes away once I let go of brakes and start driving. At idle I can get the shaking/vibration to go away when pushing on steering wheel as well as when turning to put it under load.