We don’t get many questions about noncovered shares these days, as these are primarily (though not exclusively) shares bought before 2012. The rules say you need to “elect” averaging for noncovered shares by including a statement that you’re using averaging on the return for the first year you do so for noncovered shares of that mutual fund.
Noncovered shares are treated as if they were held in a separate account, and are subject to separate averaging. If you have covered and noncovered shares in the same account, apply averaging to the two categories of shares separately. Just to be clear, though, when you sell only a portion of the noncovered shares, use the average for all the noncovered shares, not just the average for the subset of noncovered shares you sold.