OK Espresso. I believe that refers to hardware security which locks the iMac.
If I understand you correctly, the password problem occurs when you start up your boot drive.
I do not understand why it does not pop up on the iMac? A firmware lock prevents the iMac being accessed by anyone unless they have the correct password. A firmware lock is designed to prevent boot up from any unauthorised drive.
Try this on the iMac OSX.
• Close iMac then re-open into Recovery mode (hold down Command R and restart holding down the keys until the Recovery progress bar runs).
• Go to Utilities menu bar choose ‘Firmware Password Utility’
• If Firmware password is shown as On, Turn it Off. This should solve the problem.
If Firmware Password Utility is already On and you need a password to turn it off, your best option is to contact the seller again for the Firmware password or, if he has forgotten, ask him if he has the old Bill of Sale.
If that is not available ask him to write a statement giving your name as the legitimate purchaser of the iMac citing seller name, address and Apple ID associated with the sellers iMac (include serial number). He needs to sign the letter and have a friend or relative witness his signature giving their name and address as well. Same as signing any legal document.
This should satisfy Apple who can check their records for authenticity. When Apple is satisfied, they can bypass the lock with their magic tools. There will be no charge.
Personally, I would assume Firmware Password is Off. Which in turn makes me wonder how it can be required for your external SSD if it is not required for the iMac. Could it be an incompatible caddy or cable? Is the caddy advertised as Mac compatible? Something very weird going on here. I would be very interested to read comments by readers more experienced than me.
Cheers.
