Powering an LED with a Thermoelectric Generator
Here is some interesting data from a 30mm RC12-2.5 module. (One of the few that actually publishes the numbers.)



Note the 8mW output at body temps.. You would need closer to 20mW to light up an LED. The optimum voltage produced is also far too small.

Unfortunately, peltiers are much less efficient at generation than they are at cooling.