Best way to repair damaged sensor wires on lab equipment

[Ghost25]

I have a piece of lab equipment I am trying to repair, it's an Applied Biosystems Veriti 96 Thermocycler. The problem is that it gives error codes "Error Number: 0x8013 Data: 0x00,0x00,0x00,0x00" which are related to the lid and refuses to run. I found some good info here: https://www.labwrench.com/thread/135279/veriti-96?page=2

Apparently others have reported that this issue happens because the wires are bent at the lid hinge every time the lid is opened or closed and this causes the wires to become damaged and  lead to an open circuit. Apparently the green wire is ground, the blue and black are to a thermal overload device, and the purple and white are across the temperature sensor. A user reported that the resistance across the blue and black should be 7ohms and across white and purple should be 10Kohms at 25C. I measured the resistance across the wires by removing the clip and that seems about right.

I think I saw the resistance across the blue and black go to overload when I closed the lid which makes me think the issue is there, but it's hard to say for sure since it could be that I momentarily moved the probe off the lead as I closed the lid.

I was able to get the machine to run by removing the lid housing and the shrink wrap around the wires and moving them so they are not bending in the same spot as always. So I'm fairly confident it's an issue with the wires leading to the lid.

I'm thinking the best option is to splice some new wire in the middle region, I think it's the blue or black but again not sure. I'm also worried about using the wrong wire and messing up the resistance, also these are near a heating element that is 105C. This is what I could read on the wires:

Green: 24 AWG 1180 AWM Style
Blue: RBR-S CSA AWM A/B
Black: 300V 200C
Purple: basically unreadable
White: Style [unreadable] 24 AWG TFE 200C 300V

I think it may be this wire: https://www.iewc.com/product/000000000032044488

But where can I get a reasonable amount of this, and are they all the same? This one seems close: https://www.mcmaster.com/products/high-temperature-wire/high-temperature-thin-insulation-wire/american-wire-gauge-awg~24/length~10-ft/

I was thinking I would just buy a soldering iron (maybe a Pinecel V2?) and splice in new wire, but maybe there's a better way to troubleshoot or repair?

Photos of the wires: https://imgur.com/a/XOw1kbS

[m k]

Laser printers have a heater, junkyards should have some.
Heater element wires can be thicker, if memory serves they are not very bendy.