You are the MAN!
I checked under the battery and lo and behold, the battery acid had indeed gotten down there and eaten through the a couple of lines. The problem wasn't too bad yet, only the top yellow and red lines had failed. I patched them and layered the sheath with lots of electrical tape and then tie-wrapped the sheath to keep the e-tape from unwinding. I cleaned off the battery tray and sprayed rustproofing on all affected areas. I'm into the put-it-back-together stage now, as all my vacuum lines are again holding.
I didn't suspect this area because I had checked it about a year ago and there wasn't any problem. Do batteries vent more as they age? I'm not sure why the crud built up so much faster since last check.
Anyhow, thanks for the suggestions. I appreciate the resources this list brings to bear on our individual crises.