OK, I found out.

See the thread/conversation I just started with the subject line "Redeeming 'Old' TWA Miles" for details, but the bottom line is that for "non-Equity" miles earned between 1 July 1989 and 30 April 1998, you have until 30 April 1999 to use them for "non-Equity" awards, after which they won't expire, but they will be like Aviator miles.