Do governors have any role in ratifying federal constitutional amendments?

[President Johnson]

When a new constitutional amendment is sent to the states for ratification, do governors have any role in here? So when a State Legislature votes in favor of the amendment, does it require the governor's signature or can he veto it?

The president apparently doesn't have a formal role, though I noticed that Abraham Lincoln actually signed the 13th Amendment with his name and "approved, February ?, 1865".

[politicallefty]

Not that I'm aware of. There is no presumption of separation of powers at the state level. If a state had a unique form of government in compliance with the Constitution, it's possible.

At the federal level, what Lincoln did was just for show. It's not going to hurt anything, but it's not necessary either. It made absolutely no difference as to whether the amendment was sent to the states.

[Okay, maybe Mike Johnson is a competent parliamentarian.]

There's no formal role in the process for any executive branch official at any level other than the Archivist of the United States and the federal Secretary of State, and even those roles are ministerial and not actually required by the Constitution itself.

[Del Tachi]

Many governors would have the power to convene special sessions of the legislature for the express purpose of considering a pending constitutional amendment.

Other than that, no. 

[ReallySuper]

an interesting story tangentially related to this is when Kentucky Lt. Gov. Thelma Stovall became acting governor (because the governor, Julian Carroll, was outside the state) and vetoed the legislature's rescission of Kentucky's earlier ratification of the Equal Rights Amendment (which had itself passed in a special legislative session called by the previous governor, on a tiebreaker vote in the Senate cast by the then-lieutenant governor--none other than Julian Carroll, who would go on to take a conveniently-timed vacation outside the state as governor a few years later).

https://www.washingtonpost.com/archive/politics/1978/03/21/era-rescission-vetoed-in-kentucky/b6a72232-f433-40b5-b2be-ddd23914e204/

unfortunately this incredibly funny scenario is impossible in kentucky today since the part of the state constitution causing the lt. gov. to becoming acting governor automatically upon the governor being outside the state was tragically repealed, along with the part making the lieutenant governor the president of the senate and the tiebreaker vote. although i suppose that just makes it all the more iconic