1985 300TD - How to Repair Damaged Vacuum Hard Line?

I had a short which burnt through a vacuum hard line under the dash. After that the car wouldn't turn off. I cut out the small burnt section and reconnected the lines with a short piece of 1/8" rubber tubing. The fit seemed pretty snug but still the car only turns off after a few seconds. How can I make a good repair to the hard line? Should I be gluing the rubber tubing onto the line? The hard line is behind the steering column and very hard to access, so the simpler the better.

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