Being as your using a gutted caddy we have no idea if that caddy is good, bad or just does not like the drive in the first place.
Back when we had only IDE drive you could never be guaranteed the caddy you bought would play nice with say a Maxtor drive worked just fine but you put in an old Seagate and no dice. I have boxes and boxes of them in the old forgotten computer parts pile.
Out of all of the external setups I have the most reliable is the link below. I have relied on it for over 20 years and just works.
Even if the drive is toast but the platter still spins the PC would react to the drive if the caddy is sending information.
The computer would freeze until you unplugged bad drive.
The drive would show up and say it need to be formatted.
If the drive showed up and is greyed out and you clicked on it you would get the forever green bar trying to read the drive.
But that's only if the caddy is sending the information to the PC.
If the drive is just dead you would get nothing. No spinning you can feel and hear from the drive and PC might not even react.
Also I have seen some external hard drives that were sold as a unit not work unless the drive that came with the caddy was in the caddy. Same as the hard drive will not work out of the caddy.
On a side note the Master/ slave/ cable select jumper is still on the IDE drive?
https://www.ebay.com/itm/2753760359...MrC3YKOVbC-4RBZyPdK-Mr1t3bAYgd-RoC-wMQAvD_BwE