The issue here is that you set the 430EX II to slave mode. You need to set up the flash so that it thinks it's on a camera hotshoe (i.e., take it out of slave mode).

The wireless modes in the 430EX II are only for Canon's "smart" optical wireless system. Putting the 430EX II into slave mode is telling it to ignore signals on its foot (where the radio trigger is) and to only "listen" to the sensor under the red panel on the front. The CT16 Tx/Rx are faking being a flash foot (transmitter on the camera) and a camera hotshoe (receiver on the flash's foot) to get remote firing.

Similarly, if you have any wireless flash settings set in the camera menus? Those won't work. You need to set the camera as if it were using a flash on-camera. The CT16s are manual single-pin triggers (that's why they're "compatible" with multiple camera brands), so they don't speak "Canon" (or "Nikon" or any other specific brand communication). You can't use them for TTL, HSS, or remote power control.

Some TTL radio triggers, like, say, using a Godox X1R-C receiver with an XPro-C transmitter would let you use the camera menu wireless flash settings to remotely control the 430EX II, but this is relatively unique to Canon (whose flash system is apparently either the easiest or most popular target for Chinese 3rd party companies to reverse engineer) and often won't work for other camera brands.

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Addendum from comments:

Can[not] use flash menu for external settings. Says incompatible flash or flash power off.

Yes. The CT-16 are single-pin manual triggers. They cannot talk to the camera's flash control menus. That requires the four other pins and electronics to talk to the camera that it doesn't have.

Took apart the receiver to try to connect flash single bottom pin and receiver pin. This works when I do that but still doesn’t work when I press the trigger. Trigger and receiver communication good both on and off camera.

This puzzles me. I see no earthly reason why you'd do this, and you may have broken the receiver by disassembling it, given your later reports of having to apply pressure at an angle to get things to work. If you want to test whether something works properly for sync, simply shorting the sync signal to ground with a piece of wire should do it. On a hotshoe, it's the center contact that's sync and the rails that are ground; on a flash/transmitter foot, it's the center pin that's sync and the contact for the rails that's ground.

Don't do this with a vintage (pre-digital) speedlight though, unless you've measured the sync voltage as safe. With some older flashes, you could get zapped with >250V doing this.

Tried to fit the shoe backwards on flash to match the bottom pins.

If the pins match the contacts, that's not backwards, that's the correct orientation. :D You may have initially had the trigger on backwards, which is why it wouldn't fire.

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• footenote: the Godox CT16 triggers are incompatible with Godox's Godox 2.4 GHz system because they're 433 MHz. But the FC16 triggers, despite being 2.4 GHz, are also incompatible with the X system gear. Bandwidth is not the same as communication protocol.