Based on a 2019: This is a tricky one. The puddle lights are driven directly from the Driver and Passenger Door Module (DDM AND PDM) which are in the doors.
The DDM is powered, for example, from fuse F25 (30A) which is hot at all times (most modules appear to be that way). Obviously, tapping off that is not going to work.
however, the drawings also have Navigator wiring, which indicates there are ‘Scuff plate lamps’. This is powered from the BCM (puddle lamp FET). For interest, pin 26 on connector C2280C (VT - violet wire, 22 gauge, circuit CLN25. Goes to a distribution point S358 for door handle illumination as well as scuff plate illumination for both sides). It’s likely that even if you can get to the BCM connector, the pin likely doesn’t exist on a standard Expedition, and even if it does, the FET control may not be programmed.
if the FET is programmed and wiring in place, it’ll be connector C3369, a 2 pin connector for the drivers side and C3370 on passenger side. It appears these connectors should be present on the expedition (don’t know why, as the connections to them say Navigator only). These connectors are where the running board controller is under the drivers side door opening (doesn’t show C3370 for the Expedition on the passenger side for some reason). If you find the connector, it should have a violet and a black wire going to it.
There are about half a dozen drawings to look at to get the above info (only attached one image then realized this isn’t going to me a trivial task). If you are serious about it, I’d get a copy of the electrical schematics: it ain’t pretty at around 2” thick (actually, 1.77”, but whatever).
I’d like to say, hope that helps, but it probably doesn’t…
TL;DR. This ain’t your great grandpa’s pickup truck.