I have experimented with this a little.

For the units with AA NiCads, the first thing to note is that they are low capacity cells, typically 600 mAh. You can plunk a NiMH battery in there, it doesn't have to be a NiCad. But if you plunk a high-capacity NiMH in there (most good ones are in the 2000-2500 mAh range), you're going to be disappointed. You will get better results with cheapo, low-capacity NiMH cell. I get mine for a buck apiece at the local dollar store (Dollarama in my case, 800 mAh and claim to be low self-discharge).

The other thing is that (at least on the units I've messed with), the direct output voltage of the solar panel is higher than the voltage that the circuit pumps to the battery. Maybe that extends the cell life in the original intended use, but it slows charging. So I direct wire the cell to the battery contacts. The kicker is that the batt should be removed at night; some panels have enough leakage that they will discharge your cell when they're not charging. Of course adding a 5-cent diode in series would solve that problem.

I haven't tested this over a long period, but I found that cycling a few cells back and forth with a modest 1-AA LED flashlight was enough to keep me "lit up" for several nights.

Hope this helps.