I have that "Black Keys Live" DVD of an old Thickfreakness era concert in Australia with Dan playing his JD Tele.
I finally got around to watching the music videos that come as bonus material. There is that bad David Cross directed video and one for Set You Free
In the Set You Free video Dan seems to be playing a Silvertone 1423 "Stratotone Jupiter" with a black pickguard or no pickguard and a LP style toggle switch instead of a blender switch. And perhaps a Gretsch tailpiece, hard to tell from the grainy, low res video quality of the video.
You can sort of make out the Silvertone logo on the headstock in this frame.

I can't find this model listed in the gear that Dan has been known to own just his Silvertone U1 and a Silvertone 1454 "Rocket".
Anyone have any info relating to Dan ever owning this guitar? Since I recently bought a Silvertone Stratotone I am all ears.

