It's weird to me to call this "doubling" instead of "mirroring" but anyway, I'm not neurodivergent, but I've always found it nice to sit with someone else in silence, reading or studying. Its a very calming experience.
Mirroring has you copying the other's actions, thus performing the same task. Doubling allows each to work on their own separate tasks, from what I've understood.
With my spouse I just call it like, "Could you be there for moral support while I rake the leaves / open bills / do whatever I don't wanna do"