Hi Stéphane
This one gets asked a lot. You'll get lots of different answers, and budgets.
My portable solution:
Primary - Jackery Explorer 240
This is a lithium ion battery (not LiFEPO4 cells) that has a pure sine-wave inverter as well which means I can use plugged in appliances as well. Downside is the capacity is quite small for a whole night and I have to top it up with other (secondary) batteries. See below.
Big plus to this system is it's regulated output, meaning you will get 12V minimum all the time until about 5% capacity before the unit switches off or voltage falls off a cliff. "Traditional" lead acid batteries keep their voltage high initially and start dropping quickly. They also have the issue where it's not recommended to discharge beyond 50%. Lithium can do down to "0" which isn't true 0 because of the built in BMS (Battery Management System)
Secondary - various LiFePO4 batteries at 12Ah, 15Ah and 20Ah. These, to me, are the future. I have them "naked" i.e. not in a case, and I use them to keep the Jackery charged throughout the night. LiFePO4 cells don't need to be regulated. They pretty much keep their voltage all the way to about 10%. They also allow a LOT more charge/discharge cycles, in the thousands (compared to the Jackery which is about 500 cycles)
In the future, I'll be getting a Bluetti EB55 or EB70 when they come on sale in the next couple of months locally. This combines the best of both worlds; Jackery portability and usability with extra features and LiFePO4 technology.
Don't forget, one of the biggest pros to lithium: weight. Check for yourself the difference in lead acid vs a LiFePO4 battery.
Mains power
For power at home, I use a simple unit from Jaycar
https://www.jaycar.com.au/12vdc-7-5a...ocket/p/MP3575
I've also got a 10A unit, but found that it was unable to supply 12V (kept pushing out 11.8 or thereabouts) so some of my gear stopped working. I need to get this replaced; maybe I just had a dud.
Now I know I just typed a lot there, and you've only asked for power to the mount. I've included all the above so you can think about powering other gear as well
If all you want to do is power the mount with a battery, Talentcell make some great portable 12V batteries and sell on Amazon. I have one for my AZGTI (thanks Lewis!) and it works a treat. You'll just need a cable for the EQ6-6. Sidereal Trading in Melbs sell a Pegasus cable that outputs from a DC plug to the EQ6-R.
I might try and test it on the EQ6-R one day as well
https://www.amazon.com.au/Talentcell.../dp/B00ME3ZH7C