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Since the Vice President is also president of the Senate, what mechanism is there to prevent him from presiding over his own impeachment trial?

Article I.3 makes no specific mention of this.

Does a federal law cover this situation?

The constitution is not explicit on this point.

If the VP is "absent" a president pro tempore is chosen (in practice the VP is nearly always absent) If the VP is on trial, this would prevent them from presiding; they would be "in the dock" so necessarily absent from the chair, and a president pro tempore would be chosen.

Having the VP preside at their own impeachment would be absurd. The Constitution is intended to be read in accordance with Common sense. "Ain't no rule says a dog can't be president". But we are expected to use a little common sense.

Mike Rappaort considers the omission of a direct instruction that the VP should not preside over their own trial to be a "textual mistake",

But when one of the textual mistakes is an absurdity, one can depart.

I think that if a VP were to be impeached, the senate would ask the chief justice to preside. They are required to do this for a Presidential impeachment trial, and I think they would want to have a Judge present for a VP trial too. The Senate is permitted to appoint anyone to preside, it does not have to be a Senator.

There is no need for federal or constitutional law excluding the VP. The Senate is a parliamentary body. It is competent to make and enforce its own rules, as provided in Article 1 Section 5 of the Constitution:

[...] Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behavior, and, with the Concurrence of two thirds, expel a member. [...]

It is highly unlikely that any part of the judicial system would be willing to review the constitutionality of the Senate appointing someone other than the VP to preside. It would be a political question, rather than a legal question. See Nixon v. United States (no, not that Nixon) for an example of a defendant challenging a different aspect of the Senate's impeachment proceedings (and losing on this basis).

As a result, if the Senate passed a rule by simple majority excluding the VP, that would likely be the end of it regardless of alleged unconstitutionality. Even assuming arguendo that such an appointment were unconstitutional, there would be no means of judicial review and so the appointment would stick regardless.