If I get the correct mental picture of how you tested for voltage at the switch I do not believe you would have seen any voltage across the switch terminals.....unless all of the following were true:The switch you tested (inside the door) was open; and the outside switch was closed; and the lamp was good; and the connection from the lamp to trailer ground was good.
A more certain method is to find a good ground (trailer frame) for one meter lead then, with the other lead, touch first one side of the inside switch, then the other.
A real common problem with outside fixtures on my TM is a poor connection inside the light fixture to ground. Using the same good frame ground as above and with both switches "on", test for voltage at the center contact of the lamp bulb socket. If voltage is there, the problem is either the bulb or the bulb socket sleeve's connection to the frame.
IMHO.
Jerry
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Essie, Jerry and Lil' Bit the Mini Schnauzer-(now replaced by TWO Mini Schnauzers, Sassy and Schotzi)
2010 TM 3326 loaded for 3 day trip, 4955# GTW, 26 gal. water, 9.5 gal. LP, 530# Tongue Wt., 15" Dual Axle, TST Tire monitor, Hensley Cub Hitch
2004 Suburban 1500, 11,100# CGVW
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