You can make the backlight on an eTrex stay on by selecting "Stays on" from the backlight timeout menu (in Setup/Display).
actually, I've got a thingy - I could make some proper measurements
Had a go, but in the absence of some fully charged NiMHs, decided against recording data and plotting graphs and all that geeky stuff.
Suffice to say, looking at my oscilloscope's calculation for RMS current draw over a 12 second period (the current waveform is complex, as you'd expect from a computer that's doing stuff, so you need to average a few seconds to get a meaningful sample) from my random mostly-used NiMHs it's averaging about 100mA with the backlight off rising to about 230mA with the backlight at full brightness. In other words, full brightness backlight more than doubles the power consumption of the eTrex 30.
Anyway, the really interesting (if unsurprising to anyone used to working with lighting) thing is that this scales non-linearly. At the lowest settings the extra current draw is barely noticeable (a few extra mA). The current draw only reaches 150mA at about 3/4 of the way up the brightness scale.
Given that when it's actually dark the minimum brightness is perfectly adequate for reading the screen by, I'd suggest that it should therefore be perfectly possible to use it with the backlight permanently on at the lowest setting, without causing the eTrex to eat batteries.