If it has an effects loop, connect effects in to effects out with an instrument cable. That'll eliminate one possibility.
If that doesn't work, physically isolate the head from the cab's vibration. If that works, then you've got either a loose/corroded internal cable or ground wire, or possibly a solder joint that's decided to let go after all these years.
Typically when something comes out of storage we like to pop the cover and check everything, unplug/unscrew everything we can find and then put it back to scrape off any corrosion, and then hit all the pots' insides with DeoxIT Fader F-series to lube them back up.
Also, yeah, it could be the tube. Does the amp let you bypass it? I would still do everything above first, though.
Hope that gives you a few ideas.