For the record, I ordered a set of Jin Ho tuners with plastic buttons since that’s who John Mann says manufactures of SE tuners. The buttons of the JH didn’t fit the SE. I measured the SE HB button shaft and it’s 4mm diameter with 3.5mm across the flats. That is apparently the same as Gotoh. I haven’t yet confirmed with parts - if Gotoh fits I’d love to get the Phase III buttons so I haven’t bought Gotoh buttons to confirm yet.