Make sure you have the stud style thermostat housing bolt on the driver side, plus the bolt mount for the end of the cruise bracket on the alternator bracket end. There's also another bolt hole an inch or two past the stud hole, but it's not critically required as long as you have the stud mount on the T-stat. There's three holes on the bracket and you really should use all of them for stability. If you use a 307 intake (earlier style larger port) manifold, it bolt up pretty much everything you had before. If you're using the 350 intake from the 350 engine, not sure what ports and bolt bosses you may have to work with so you may only be able to use the T-stat stud mount hole.
Depending on the carburetor used, you may have to rig the actuator rod to the carb linkage.
As stated, to get your cruise to work without CCC, there's a couple of ECM wires that invade the system. One is simply the VSS to the ECM to tell the ECM how fast the car is going. The other is simply a ground. There is may be a pink/black wire- that is a power supply. Don't ground that one. IIRC, it may be white/black stripe. It is on 1984/85 models. Not sure about the 86-88. But not 100% sure. Don't quote me on that. Make sure you know which one is the ground to the ECM. Just ground that wire somewhere and it should work. It fakes the system out that the ECM is "allowing" the system to operate. The issue is, when you yank out the CCC stuff, that ground could go away that the VSS ground was connected to. That big CCC plug on the passenger side of the engine contained your VSS ground, so if it's gone...so is your ground. So find your VSS ground wire that would have went to the ECM, and send it to a mounted ground somewhere and your cruise should work.
Brown I think goes to the ECM for speed input to help control lockup converter. Who cares about that one now?
Assuming you went from Olds 307 to Olds 350? Then you should have all the brackets and junk available if it was working before.