Okay. I just did another test. Mainly to get more info about the Ah usage.
The Dremel I have is with variable speed, and it turns out, that the variable speed basically did not work, when running on my modified sine wave inverter. It runs fine at full speed, but that is basically the only speed where it works.
At full speed the amp draw from a 12V battery (well, a LiFePO4 battery at 13.9V) is about 6 amp. (13.9V x 6A = 83,4W) And this is when it is just running free. The label on the Dremal says it is a 125W motor, so once I start cutting anything, I expect the amp load to get higher.
So for a corded Dremel with variable speed, I would choose a Pure Sine Wave inverter.
I see that the Dremel you have is a two speed version. That one is likely to function fine on a modified sine wave inverter, as I expect the the speed setting is not electronically controlled, but rather mechanical switching between using different spools in the motor.
Would the modified sine wave inverter bea ble to run the cordless charger? Yes I would think so, as I have run other cordless charger tools on my modified sine wave inverter, without any problem.
But back to the Ah usage, and the question of how big a battery is needed, and how little solar might be enough.
The Dremel 200
website says 120V at 0.9A = 108W
From a 12V battery that is about 9 amp. Then add some loss in the inverter and it will possibly take 10-11A per hour to run the tool. Probably a little less when the motor is only idling, and not being used for heavy cutting etc.
But lets say an average of 10A per hour.
When running at half speed, the power usage is likely to also be less, but perhaps not half.
200W solar panels might produce around 15A per hour with good sunny conditions. So while the sun is out, you could run your tool just fine. And any size battery would ensure that those few minutes without sun, your tool would keep running.
Does these Ah calculations make sense to you?
My next question would be, if you have any other power sources, for when the sun is not perfect, or when you choose to work outside daylight hours?
And as big of a (car) battery as possible might also help on those days with less than perfect sun.
A battery example
For a 33Ah battery it is advisable to only use half, in order to help the battery las as long as possible. So that is about 16Ah usable (when there is no or very limited sun). Or 1½ hour of full use, and possibly 2 maybe 3 hours of use, when the tool is at half speed.
The cordless Dremel only has limited information about the actual power of the tool, expressed in watt of the motor or watt of the battery, or how long it can typically run on a full charge.
All I can find is, that it is 12V and the battery is 1 Ah, and typically takes 3 hours to charge. And that the 8220 runs 33% longer than the 8200 - when cutting screws.
And the 8220 comes with two batteries.
So it is very difficult to guesstimate much about Ah use, only based on data from the Dremel website.
But is seems that the battery might be a 12W battery. If the tool is only half as powerful as the Dremel 200, and about 1/3 as powerful as the Dremel 300, that makes it about a 40-50W motor and at full speed, it could then run 10-15 minutes on one battery charge.
Does any of these thoughts and calculations make any sense or seem useful to you?