Check the secondary employment conditions of your main employer to ensure that part-time paid employment is 'permitted'. My main employer (NATS, bless their hearts...) made it very difficult for some (but not all...
) employees to engage in part-time paid employment particularly within aviation-related activities.
Flying schools used to be grateful for P/T FIs whom they could call upon at short notice to address a shortfall. Expect many trial lessons and do not expect much continuity with individual students. It's true that schools prefer regular and predictable availability especially at weekends. Be prepared for the remuneration to be not much above minimum wage. If you become addicted it could put a strain on domestics.