You said your Power Tank is fairly new, but I'll say this anyway: rechargeable batteries do eventually "wear out" and quit taking charge. Perhaps you can find a Batteries N Bulbs Plus type of store and ask them to test the battery in your Power Tank. You might have a bad battery.
Yes, you can use mains power with your mount. You need to purchase a power supply which converts your mains (120VAC or 220VAC) to 12VDC. For just your mount, a power supply with 2A capacity should be plenty.
Could be something as simple as this (I don't know if this unit is of good quality or even if it has enough capacity, I'm only showing it as an example):
Or something like this (I use something similar when I am at star parties that supply 120V power):
If you buy a power supply make sure the plug is the correct polarity! If you plug power with the wrong polarity into your mount you will damage your mount's PC boards. I think the AV-X plug is what is called "center pin positive" (see picture below), which means the center part of the plug has + voltage and the outside of the plug has - voltage.
Edited by macdonjh, 26 March 2020 - 10:25 AM.