Some LED's are very efficient, and the eye is extremely sensitive. In a moderately lit room, a white or blue LED should be clearly visible, though not bright, with just 100 microamps. Two CR-2032 Li cells. Rated at ~200 mA/hr, this should last >2,000 hours, ~3 months. Put a 30 kilohm (kΩ) resistor in series (or even a higher resistance for a dimmer, but longer lived light). You could also use AA or AAA "penlight" cells (you'll need three or four for a white LED), and they should last a year or more.
The eye is less sensitive to red light, but a red LED can operate from a single Li coin cell. Try 15 kΩ with one Li cell.
A larger resistor decreases current, at the expense of brightness. Try a few different ones for your particular application to find a compromise that looks good on the model and lasts long enough. You might add a switch, but with very large resistors, the battery will last almost as long as if left on the shelf (5-20 years for Li-ion cells).
BTW, in a dark room, one microampere creates enough light to be seen easily.