Why don't you use QR or exporting file even loading a text form are much easier.
I know this but this is not my intention for using the cosigner pool.
neverthless u right this is quite an other possibility for sign the transaction over multiple wallets.
(at least from what I can recall in my previous test)
as far as i remember on my test mainnet 2019 at this time it wasnt the case, the pool popup had rised up immediately.
further observations (mainnet):
sometimes its not possible to send the tx to the cosigner pool ( there is no button availiable for it), then i closed the 1/2 wallet the popup from the cosigner pool appears on the 2/2 wallet without any interaction.
perhaps you might want to open one, the Devs might be able to fix/find-out the issue
i'll think about it
best regards