Hi Dawn, I have never owned that system but in a former life, I used to fix stuff. Short off the hip guess to your problem?
The two "bad" batteries might have contaminated power output connectors. Just a guess.....this is my reasoning
1. It is highly unlikely that two battery packs would fail at the same time although connectors are prone to failure.
2. I understand that your charger connects with a USB-C connector and the charger indicates that the battery is good and charged up, but this measurement would be at the USB-C connector. The power goes to the lamp on the other connector (round one) from the battery pack, which I guess could be contaminated (or damaged).
3. Since the 3rd battery pack lights the light and all works fine, the issue is not with the lamp assembly or the remote switch
4. If the good battery had been connected to the lamp, the other two might have been exposed to liquids, moisture or simply oxidized in storage.
If cleaning the round connector coming off the two bad batteries does not work, I would measure the voltage at that connection. Don't jam something metal into the connector, you could short the battery. I would use a small piece of very fine sandpaper myself. Try to find a local friend with voltage meter to check it, assuming you don't have a meter (again using care not to short the battery). It is possible you have bad cells in each of the two bad battery packs but I doubt it since Gemini uses very high quality batteries, the best actually. I understand the 18650 cells inside the pack are replaceable. I think Amazon might have your battery pack if you cannot find the problem. Hope this helps.