Will the Houthis join Iran in war against Israel and the US?

As the US-Israeli war against Iran drags on, Yemen's Ansarullah, or the Houthis, have stayed out of the conflict. But that could change. They have said they consider themselves directly concerned and could take a position alongside Iran. The armed group has attacked Israel and shipping in the Red Sea in recent years. If a new front opens up, global trade could be further disrupted in another maritime gateway. Shipping is already largely halted in the Strait of Hormuz, causing significant losses worldwide. So, will the Houthis join the war? And what difference could that make for this volatile region?