So today I called T's phone number to hear his vacation message. (Can't believe I haven't done this before now!)

He gave his away dates and the name and phone number of a covering T.

Personally, I wouldn't call this covering T under any circumstance that I could possibly imagine. If I had a huge emergency like a death or something I think I would call T's cell phone and leave a message. If he didn't call back, then I still wouldn't call the covering T. I mean, the whole thing is the personal relationship, so how could a covering T possibly help?

Under what circumstance would you call a covering T?

1 week 5 days till my next appointment
1 week 1 day till I can call