With Morton's Neuroma, what causes the clicking (Mulder's click?)? I sometimes get a clicking in the toes that causes pain

That's the neuroma . Itself rubbing on the deep transverse metatarsal ligament, some argue the neuroma rubbing on the metatarsal heads, in either case it is felt to be pathoneumonic for diagnosing the neuroma. .
Popping nerve. With a Morton's neuroma, the nerve is enlarged. This enlargement is between the metatarsal bone heads. With side to side pressure or in tight shoes with walking , the enlarged nerve is squeezed and pops back and forth between these bone causing these popping sensations. This is even a diagnostic exam test called a Mulder's sign.