My renters are moving out and I believe it will take at least 3 months to sell the house. The mortgage is $63k at 7% interest and the house will probably sell for $145k. The reason I'm thinking to do this is to save on the interest (which is $371/month) during the months when it's unoccupied. Possibly saving a total of $1,113 over 3 months. I think it makes sense, especially if it's longer than 3 months but I'm unsure about any tax implications or how it might affect the capital gains or fees I might pay during the sale.
Since this is a rental property you can deduct the mortgage interest, so note that your true savings is actually less than $1113. (Reduce it by your effective tax rate, e.g. 25% total tax rate means your actual savings would be $835.)
Regardless, if you have the cash sitting in the bank you might as well pay it off. You'll get it back soon anyway. Another way of thinking about this is if you had the option of putting that $63K into a 3-month CD earning 7% APY, would you do it? I'm guessing you would.
It depends. If paying off the mortgage will leave you 'cash poor', i.e. under 6 months living expenses left in your account, then definitely not. (The sale could take many months or even years if it is in an undesirable area or there is a crash).
If, on the other hand, you have plenty of cash left after paying it off, then there is no reason not to, as TTT mentions, you effectively get a 7% return on your investment for x months.