Shaky Drivers side mirror and TPMS light issues

I have two issues currently with my tundra.
The first is that the driver's side mirror is shaky enough at highway speeds that it's difficult to use. Where the housing meets the door frame, it appears to be properly tight with no movement, but the joint where the mirror folds in and out appears to be slightly looser than that of the passenger side. The actual glass also appears to move slightly more than the passenger. Are there screws that hold this joint that are able to be tightened? Having trouble finding any info on it.
The second issue is that my TPMS sensors are not functioning properly. When the key is tuned on the indicator flashes for about a minute before becoming solid, and stays on the rest of the time that the key is on. I looked in the owner's manual, which said that this meant an issue with the sensors and to take it to a dealer to be fixed. I figured that would probably cost an arm and leg for them to replace them. Any other suggestions to try?
Thank yall for the help!