Looks like we're form the same era!
After scrubbing the tires I would put a light coat of liquid floor wax on the sidewall. The next time I cleaned my car I would scrubb the tires again with Comet and then apply the wax again. It would give the rubber a nice wet "shine".

 

Wow this is an interesting thread..i cant imagine using comet on anything...i know things get really dirty but like others mentioned there are a lot of other routes that can yield the same results..even with a cleaner this abrasive and dangerous..your tires and wheels can only get *so* clean. For the tires Simple Green 1:1 is a great option and readily available...but wheels i feel can get a bit tricky.. for most factory wheels you can get away with a bit more but aftermarket are a different story. If you do any other vehicles you ahve to have a regimen that agrees with all surfaces..here is something that i have found to be excellent...but gurus please chime in if u think this isnt a good option:

I take a car wash soap that i have fallen out of love with. In my case it would be Meguiar's D-Line Shampoo plus. I dilute 1:1 with water (yes 1:1) and use it as a degreaser. As always keep this kinda dilution rate off of the paint but i feel that instead of harmful chemicals i use a strong version of safe ones even for tough grit and nasty