Keep a record of searching for work - your partner could advertise his musical skills on social media fulfilling the ask of obtaining work, where possible, and in the current situation we all know how hard that will be.
Creating a CV and circulating to wedding venues etc is demonstrating searching for work- weddings are currently limited as we know.
Your clause does not state he must look for work in areas away from his normal employment so they cannot force this, but you could show willingness to comply. This time of year supermarket's do seek evening workers to help replenish shelves - it maybe worth a CV being sent to demonstrate searching for new and alternative work, but unlikely you would hear back from them
