There is a lot of neck pickup tone in some of the solo passages in that song. Most of it however, is the in between position (bridge/middle).
Not familiar at all with the DS2. Stevie used TS pedals most of the time. FWIW, he wasn't concerned with the vintage models so much. When the 808 was new, he used that. When the TS9 was new, he used that. He even did lots of shows with the TS10 when it dropped.
The mid hump of those TS style pedals does a lot for beefing up the naturally scooped sound of a Fender amp.
IMO, the way to the SRV style tone is NOT with a neck pickup and a cranked up TS. That's way too dark to get into his territory.
SRV used all the positions on his switch, but really did a ton of stuff in the bridge/middle switch position. His tones are also incredibly bright a lot of the time, especially on the Texas Flood album. His technique for setting up an amp in those days was to use a Blackface like a Super Reverb or Vibroverb, and to turn it way, way up. The intro and rhythm tracking on that song is textbook Blackface cranked to the "annihilate" level, with no dirtbox.
He would set the tone of the amp, by turning it up, and jack hammering the low E string. He eq'd the whole amp around that low E. When it was sounding tight, with no flub or fart, and loud as hell, then the amp was right. That makes for a hella bright tone most of the time. Watch Live at the El Macambo for a great example of this.
With the amps set like that, the TS pedal didn't need much gain on it at all. It was almost used more as a clean boost, with the volume up and the gain down. It just pushed an already red hot amp over the edge.
If you want that tone at useable club gig volumes, IMO it can't be done. but you can get really close. Brighten up the amp, and try spending a lot of time in that #4 position with the bridge and middle together, and dig in really deep. Stevie's hand were like vice grips. Don't know what gauge strings you use, but I get WAY closer to his thing with 11's than with anything lighter. I used to play 12's, but can't do it anymore. Resist the urge to use too much gain. 99% of the time, SRV's tone is a lot cleaner than it sounds to the casual listener. later in his career when he got into the Dumbles his tone really gained up and got muddy, and I thought, suffered a lot. You can hear an example of that on the "Live From Austin,TX" video, the later ACL appearance was all that muddy Dumble thing. The pure cranked Blackface thing from the Texas Flood album is where it's at for me.