Godox TT350n/Nikon D610 - How to fire my Godox flash "only" as a rear curtain sync?

Can someone help me find the right settings please?

You don't need the right settings, you need the right trigger.

Your flash is set to receive a radio signal from a radio transmitter.

You need a Godox compatible 2.4GHz radio transmitter with a Nikon compatible hot foot mounted on your camera's hot shoe to trigger the flash in radio mode. You can use a dedicated radio transmitter such as the Godox XPro or X1T, or you can use another Godox 2.4GHz radio flash capable of second curtain sync that can act as a controller.

The Godox TT350 is not capable of being controlled optically via Nikon's CLS/AWL wireless optical communication. You can't do second curtain sync with the TT350 using optical control. The TT350 does have "dumb" optical S1 and S2 "slave" modes. But in "dumb" optical mode, the flash will fire as soon as it detects what it interprets to be the "main" flash from another bright light source.

Bought X1T-N, still can't seem to fire my TT350-N through the transmitter. Is there any additional setting that I need to take care of to hook them both up? Setting on X1T-N: Group: A Channel: 1 Setting on TT350-N: Group: A Channel: 1 Sync: Slave mode

If either unit has the capability of setting "Wireless ID number" have you checked to confirm that both are the same? If one doesn't have "Wireless ID number" capability and the other does, the one with "Wireless ID number" capability should have the "ID number" set to "off."

You are an absolute legend @MichaelC - No one on the internet talks about ID stuff. The ID on TT350-N was set to 1 (doesn't go below 1) and on X1T-N it was set to 0. I made both 1 and they're working now. :)

Commander mode is for Nikon's optical CLS system or their radio WR system. It does not work with Godox's 2.4 GHz radio system. While the Godox TT685-N and V860 II-N full-sized speedlights can be optical CLS commanders/slaves, the TT350-N/V350-N cannot.

Your TT350-N is set into radio master mode [antenna icon in lower left with M], to be used as a transmitter on your camera's hotshoe. To get it to work as a radio slave, you also need a Godox transmitter for the camera hotshoe (e.g., XPro-N, X2T-N, Flashpoint R2 Pro II-N). The transmitter should let you set 2nd curtain; instead of using the camera menus to set wireless control, you'd use the transmitter's UI instead.

If you do get a Godox transmitter, you would need to set the TT350-N to radio slave mode by holding down the SYNC button, and when the radio icon flashes, use the wheel/SET button to cycle through M/S/off.

You can trip the TT350 off-camera with your pop-up flash (out of Commander mode, and in M/TTL) by using the S1/S2 "dumb" optical slave modes (be in M mode, no radio function set, and use the SLAVE button on the TT350), but these are similar to SU-4 mode, and do not allow for TTL/HSS communication, and possibly do not allow 2nd curtain (depends on when the pop-up flash burst fires). You may also need to take the TT350 out of radio slave mode for this.

See also: My Godox flash won't fire off-camera. What should I check?

If you are using the built-in flash as your trigger, it has to fire. That's how optical triggering works.

You can use a different trigger (radio, cable), or you can use a hard IR-pass filter like Nikon's SG-3IR to prevent the visible triggering flash from affecting your exposure. Going with a radio trigger, preferably one that works directly with your flash, will be the better option.