If an Ethereum address is a point on the Bitcoin EC, then one can use the private key that matches that address to sign a message using bitcoin software.
I'd like someone to prove they have the private key for an ethereum address by signing something with it and I don't know how one would sign a message with an ethereum address. I found https://etherscan.io/verifySig where such a signature can be verified.
If I export the private key for my ethereum address and then import it into a Bitcoin client and then sign a message with it, will that be valid according to etherscan's verifySig page?
If I simply restore my wallet to a Bitcoin client using my Bip39 phrase, then can I sign something with the bitcoin address at a certain derivation path to produce a valid signature under ethereum for the address at the same derivation path?