Just something to consider, an idea I'll be trying myself at some stage... conductive paint.
What about insetting a 3mm led into the wood itself before you add the resin?
Drill 2 very small diameter (1/2mm) holes through the wood base to the bottom of the LED pins. Set the LED in place, then inject contact paint through the holes with a syringe, allow it to set, making contact with the bottom of the 2 LED pins. That way, you have an electrical contact running through the wood to the LED. Test the connection, then add the resin and turn, finish the piece.
Then, if you set 2 tiny contact plates (+ve and -ve) into your base (foil etc?), it will complete the circuit when your contact paint in the piece touches the contact plates, and the light will come on. The light will go off when you pick up the piece. You can put the resistor in the base, soldered to the positive connection, between the battery and the contact plate.
The only thing to make sure of is that when you wax/polish/lacquer to finish, you don't get any on the contact paint at the bottom of the piece, or it will create a barrier to the circuit and break the contact.
Mad, quite probably.
Adventurous/creative, definately.
(see
https://www.kitronik.co.uk/4804-bare-conductive-paint-10ml-pen.html)