At our week long elder's meeting just two years ago, this came up. The instructor asked: how is it that elders are appointed by holy spirit? From my recollection, here's the basic process.
1. Elders pray for holy spirit when they are reviewing brothers' qualifications. The holy spirit can act during that meeting on any elder to bring up something that may disqualify a brother.
2. Elders pray again at the meeting with the C.O. for holy spirit when actually making the recommendation. Holy spirit can act during that meeting, especially on the C.O. as he observes the brother during the week.
3. When the recommendation is sent into the service department, the brother getting the recommendation form may have something jogged in his memory. Perhaps the brother's name was in front of him before. He will look at the files there at the branch. Holy spirit may direct him to some information that could disqualify a brother.
4. The brother is approved by the branch, and the approval is sent back. The brother is asked the standard questions about whether there is anything that would prevent him from serving. Holy spirit may act on that brother right then and there if something is a problem.
Funny, now that I've written it down, it appears that holy spirit takes an active role in deciding whether a brother should NOT be appointed. LOL!
So, yes, they absolutely teach that elders are appointed by holy spirit. In addition, (not sure whether this was already mentioned), but there is a recent reference to this teaching:
w12 10/15 p. 14 par. 8:
Thus, as Head of the Christian congregation, Jesus has full control of the bodies of elders. If someone on a body truly needs correction, the One who has “eyes as a fiery flame” will see to it that this is done in His own time and way. (Rev. 1:14) In the meantime, we maintain proper respect for those appointed by holy spirit, for Paul wrote: “Be obedient to those who are taking the lead among you and be submissive, for they are keeping watch over your souls as those who will render an account; that they may do this with joy and not with sighing, for this would be damaging to you.”—Heb. 13:17.