bmaverick, Most regulators are mounted on the firewall. Is yours not there?
It's mounted inside the dash near the steering wheel column shaft. It's on the right side of the steering shaft. The 2-way flasher is nearby too. On the left side, the Hour/RPM meter hogs up a good chunk of space in there.
Look at page 83 in the YANMAR YM2610 PARTS CATALOG NPC-1058.pdf
Page 83 shows item-1 as the wire-harness. Just above the "1" on the same side is the VR connector. I've browsed a few pages, yet don't see the VR in the diagrams. Bet it's one of those "*" or "I" part numbers one has to find in the back sheets of the parts manual.
I've been behind that dash access panel more than I ever wanted. LOL Fixed the 3 bulbs from Hoye, another time repaired the decompression cable as it snapped in half, 2 separate times clearing out a mouse and the next year a bird nest, and looked to see how to hook up the horn. Don't recall if I ever took a pix with that panel off.
The VR looks to be the original OE 124550-77710.
Fredricks does have the modern replacement

VR-550
Voltage regulator – Our NEW solid state regulator
replaces the old mechanical type. 195, 240, 330, 336,
1700, 2000, 2200, 2210, 2500, 2610, 2700,
3000, 3110, 3810, 4300 Repl. 124550-77710
Voltage regulator - VR-55 - Fredricks Equipment Parts - Your home for Yanmar, Mahindra, and Bad Boy Mower parts!