Brian Wilson has two saves and two losses in MLB doubleheader games going into today’s split bill between the Dodgers and Twins.
The chart below uses ESPN’s doubleheader resource and shows managers used Weez in six of the eight doubleheaders when Wilson has been available on the roster (I think).
Doubleheaders during Brian Wilson's career

There are lots of factors — the score of the game, the performance of the starter, a player’s recent workload — that affect a manager’s decision to call a pitcher from the bullpen.
If Don Mattingly brings in the beard in one of today’s doubleheaders, and the chart suggests he probably will, I’d guess it would be in the second game. Remember, B-Weez threw only 14 pitches and struck out two Twins in the 8th inning last night.