Tying in to the "light circuit somehow" is the issue.
autozone has alot of wiring diagrams you can access on-line, specific to Rangers by year.
You don't mention the year of the Ranger but it is most likely that if it is a timed circuit then that timer would be in the GEM(generic electronic module), located behind the radio.
The Dome light is on relay most likely but it would only have 1 trigger wire coming from the GEM, so the GEM would decide if it will be a timed closure(door unlock) or a fixed closer(manually turn on dome light), depending on which trigger was received, unlock or manual switch, so you would need to find that trigger BUT that probably wouldn't help because you would then need 2 relays, one to sense the unlock trigger to close the relay to the dome light, and that trigger is only momentary so you would still need the timer.
Best to just get a relay with built-in adjustable timer and match it to dome light timer.