I would go with a peel and stick single led strip light inside the top front of the cabinet (next to door, dacing towards the back). They can be cut to the needed lenght with scissors and are as cheap as 3 buck for 16 ft. With just the 3 buck lights you could havest 12v power from a near existing light, or spend 20 bucks for one with a 120v to 12v transformer that includes a wireless remote.
I swaped out a bad set of awning leds (waterproof) for less then 20 bucks.
Hoglou the DH & BK the DW (retired and happy)
WestGA KM4HQQ 146.640mhz
L'IL Foot" 2014 Sunseeker 2300
"Harry" the JK toad in the mirror
Check out the "mods" in the albums