Most of Timmons tone comes from the amp settings he uses, as he played most of his career with a Seymour Duncan JB. If you listen to some old tracks from him, you'll notice that his tone was way more bright than it is now. He said in a couple of videos that he rolled off most of the highs and presence of the amps he used, besides his current Mesa Rig (which doesn't need that).
I have a bolt-on jackson with a Duncan JB that can nail Timmons tone better than any of my guitars. Perhaps a Rebel Yell will work for you.
For the neck pickups, he uses some Dimarzio single-coil sized humbuckers with very little output, as he uses the neck pickup for the quiet stuff. He also has a specific capacitor installed to bleed some highs when turning the volume down, to retain warmth on the clean tones. I'm not sure which single coil pickups would do best here, as I'm certainly not an expert on those.