I got a written response from the State of TX: No tax is due because this
falls under the "occasional sale" exemption. Second hand kit, both of us
individuals, neither engaged in the business of selling stuff.

QUOTE:
The purchase of an aircraft kit and/or aircraft parts and materials may be
exempt as an occasional sale under Tax Code Section 151.304(b)(1) provided:

1) the seller has not made more than two sales of taxable items (not just
parts for an aircraft) subject to sales tax within a 12-month period, and
the seller is not engaged in the business of selling taxable items (not just
aircraft parts) and 2) neither the seller nor the buyer has been issued a
sales tax permit or the equivalent by Texas or any other state.

In other words the purchase, in one or two transactions in a 12-month
period, of parts and materials to build an aircraft by an individual who
does not hold a sales tax permit from another individual who also does not
hold a sales tax permit, is exempt from Texas sales and use tax as an
occasional sale. However, the subsequent purchase of such parts and
materials by the same purchaser from the same seller will be subject to
Texas use tax if brought or delivered into Texas. See Rule 3.316 on
occasional sales.

END QUOTE