Motorcycle Repair: tough bolt, speedometer cable, screw out

Question
Jon I sure hope you have an idea on this one. I own a 1983 Honda Shadow vt500. I'm trying to lube the tach cable but I can't get the retaining screw out so I can pull the cable out to lube it. The screw has a phillips head that is starting to round off because of so many tries to loosen it. It is also in a hard to reach location, on top of the front engine head. The cable is making a whirring sound when cold but goes away after it runs awile. I just don't want it to break. It's probably never been lubed since when I did the speedometer cable I could tell the cable was all gummed up with black junk, probably the old lubricant. Please give me some idea how to get this bolt out. I'm going to replace it, if I get it out, with a hex head screw. That way a socket would be much easier to use. Thanks for being there for me. Tom

Answer
These little problems can be the most aggravating, time consuming, fiddly, and depressing jobs on a motor cycle. I know too well. The most logical solution, which depends on the access to the retaining screw in question. Which you say is not good, is If you can get a small drill in their, maybe even a "dremel" mini tool, or similar, you could utilize a screw removing tool, a small left handed thread which taps anti clockwise down into the top of the offending screw, and the insert tightened until eventually the screw will be screwed out as the insert gets tighter. You may well know, or have thought of that, as I said, it depends on access, you could use a flexible drive on the mini drill if it helps. Other options to try, again access depending, a little WD40 down into the threads, then carefully use an impact screwdriver, with an as best fitting bit you can find to fit the damaged phillips head, if you can safely apply a little heat beforehand to the surround of the screw, it would help, but of course any plastic nearby will need to be avoided, or if possible shielded from the heat. You gotta be careful though if you try that to protect any surrounding alloy or fittings from a wayward strike. Sometimes I have just  had to resort to a basic small hammer and a blunt chisel, gently, like a stonemason might work, form on the outer edge of the screw a groove with the chisel, (not too sharp as to shear away the metal) and tap, gently anti clockwise, big hits don't work, little by little, and eventually it will break free, and when it does, you will feel soo satisfied with your handiwork!

In conclusion the best way is if you can get a screw extractor in there, you might need to accept that some removal of access restricting parts may be needed.

These situations can be difficult to suggest an instant solution to, it might be in real tight, or just ready to break away, it's really a matter of persisting, and being patient, you will win in the end!!
Good luck