Good deal on the Eastwood and it will be good. The white sealer is, I believe, a round ribbon of puddy that could be used as a water shield in those areas. I think it stays pliable. Maybe like plumbers puddy. But I’m no expert like some here, just a shade tree taught, but learning son of a gun.
I assume you are speaking of strip caulk. It doesn't really seem like that to me as I am used to this stuff staying rather gooey, even over time. That stuff I removed was very tough.
I took a look in the FSM and at the beginning of seam sealer section, they talk about "Body Seam Sealers (for exterior sealing)" and "Heavy Sealing Putty (for interior sealing)", which does sound a bit like strip caulk. And then they go on to describe certain interior sealing areas as "bead" sealer and then "ball" sealer, which I would assume is referring to the two sealers mentioned...respectively. The diagrams below, where they refer to "ball" sealer is exactly where I found this stuff. Although I did find it used all along the seam where the front floor pan meets the firewall.
I included some of my own pics of this stuff and as funny as this sounds, I did find a fingerprint in the putty where they clearly mashed this "ball" sealer into this area during its assembly. That does seem to indicate this was once a putty like substance that over time became rock hard. Either this is some special stuff that's no longer available/used or it is similar (if not the exact same) as the stuff we know as strip caulk. And maybe this stuff does get somewhat petrified after years and years and becomes rock hard. The other important point that I had mentioned earlier is that all of these areas were bare metal, including the floor to firewall seam.