Gerunds/present participles of two-verb compounds

Solution 1:

Collins indicates that it's the first simplex verb in this extraordinary compound verb that is conjugated:

make believe [verb]

to pretend or enact a fantasy

• the children made believe they were doctors

As this is contrary to the licensing at Lexico, this is obviously a grey area. For what it's worth, I think that 'made believe' sounds far better than 'make-believed', but 'making believe' doesn't sound too hot.

The use of 'make believe' as a verb is far from common, and its conjugation thus uncertain. The availability of open and hyphenated forms adds to the uncertainty.