Apple - Do USB-C to Thunderbolt 2 cables exist?

I don't think a straight-up cable exists, no. However, you can get an adapter/dongle that works perfectly well for your scenario. You'll need to Apple Thunderbolt 3 (USB-C) to Thunderbolt 2 adapter:

https://www.apple.com/us_smb_83039/shop/product/MMEL2AM/A/thunderbolt-3-usb-c-to-thunderbolt-2-adapter

You can read more about the adapter here:

https://support.apple.com/en-gb/HT207266

Note that Target Display Mode is not using the same kind of signal as mini-DisplayPort - therefore a USB-C to mini-DisplayPort cable will not work! It needs to be an actual Thunderbolt 2 source.

You're not going to find a Thunderbolt 3 to Thunderbolt 2 cable as an adapter is required to connect to legacy devices.

One of the (major) differentiators between Thunderbolt 1/2 and Thunderbolt 3 is that Thunderbolt 1/2 required the cable to be active (it required power to operate) whereas Thunderbolt 3 can use standard USB Type C cables (it's passive)¹.

With these older Thunderbolt standards, the cable was active, meaning the cable itself is a device that requires power to operate (which is why most Thunderbolt 1 or 2 devices would require an external power source in order to function.)

Thunderbolt 3 is backward compatible, but will require an adapter.²

From the FAQ:

Is Thunderbolt 3 backwards compatible with Thunderbolt and Thunderbolt 2?

Yes, solutions and products built to Thunderbolt and Thunderbolt 2 specifications will work with Thunderbolt 3 via an adapter.

^{(emphasis mine)}

To make your setup work, something like the StarTech TBT3TBTADAP TB 3 to Legacy TB adapter.

I've personally used this adapter to connect a 2018 MacBook Pro to a legacy (Thunderbolt 1) WD MyBook Duo and it worked with no issues.

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Note

This kind of adapter is only compatible with Thunderbolt devices, not Mini DisplayPort.

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¹ C|Net: USB Type-C and Thunderbolt 3: One port to connect them all

² Thunderbolt Technology Frequently Asked Questions