Those look like IDC connectors, the wires should just pull out. If the pin is bad/corroded/broke I have not seen IDC replacements and I don't know if the crimp ones fit in that same housing. i need to find out though as I have a project Time Line that I need to do some pin work on.

I just went and checked out my Time Line, which is actually the first time I've looked at it since I picked it up, and it appears that the standard crimp-on card edge connectors will fit in that housing. I tried one I had and it appears to work in the one I know was broken. On inspection a couple of the other connectors housings have had them replaced with the crimp on ones. you should not need new housings, just new contacts.

I believe they are https://www.greatplainselectronics.com/proddetail.asp?prod=08-52-0072&cat=77
or https://www.greatplainselectronics.com/proddetail.asp?prod=08-50-0134&cat=77 depending on wire size.

pic of broken idc type connector on top and crimp on connector on bottom.

IMG_20190213_160039 (resized).jpg