Quite honestly I believe most of the sound can be found in the Rick pickups. I have put authentic Rick pickups in a few of my basses and they sound way more like Rickenbackers than the cheap Chinese Rick copy I own, in fact my Thunderbacker sounds more like a Rick than the Peavey t-40 witch comes with a built in Rick tone. If you still arent convinced check this out.
A cool video! The Rick pickup in the neck position of that Jazz bass sounds like a 4003. The bridge pickup doens't, because it is far closer to the bridge than the pickup on a 4003. Likewise the pickups are in the 'wrong' place on your Thunderbird, though it is probably easier to EQ it this way, and it looks very cool.
I don't buy the notion that a T-40 sounds like a Rick. It does, a bit, but they aren't the affordable Rick substitutes that some claim. You get a deep but articulate tone from the neck pickup of one, which might be a perceived generic Rickenbacker tone. However I've not heard any combination of the two pickups on a T40 that sounds like a Rick with both pickups on.