Resident mathematician here. Any pit controller (BBQ Guru, Billows, ...) is implementing a classic feedback mechanism:
proportional–integral–derivative controller
If your fan is always on at 200 F, always off at 240 F, and on part of the time in between, proportionate to the pit temperature, then your pit will stabilize at some temperature between 200 F and 240 F. Where? It depends on everything. Same as a hiker climbing a mountain, and a hiker descending a mountain, they have to cross paths somewhere. Not necessarily at the halfway point, just somewhere along the trail.
Suppose that you want to stabilize at exactly 220 F? The PID mechanism learns the system it's controlling, and adjusts the fan rate to nudge where your pit stabilizes.
Every pit is different. It doesn't matter, the PID mechanism figures it out. I have several sizes of fans for my BBQ Guru. It doesn't matter, the PID mechanism figures it out.
Here we get abstract. Abstraction is easy, it's forgetting part of a problem that turns out to be irrelevant. Here, your PID controller sees the effect of turning a system on and off at regular intervals, as measured by the pit thermometer. It has no clue what your pit looks like. It has no clue what your fan looks like. It sees a system, as a black box that it controls.
Where am I going with this? If the Signals fan output is 12V like all standard computer case fans, then it can control any fan you like, such as a BBQ Guru fan that happens to perfectly fit the existing Guru port in our KKs.
There are several complications here. First, there are two flavors of fan control: On/off, and pulse code modulation. In other words, one could run a fan faster or slower as needed, rather than cycling it on and off. The BBQ Guru fan doesn't support this. Can anyone who has a Billows tell us? Does it run at a variable rate, or does it cycle on and off?
Second, we have a cabling problem. The Billows connects via a USB-C cable to the fan adapter. Now, frequently USB-C is used merely for charging, in which case we need to splice the appropriate wires on a USB-C cable to make something a Guru fan can plug into.
Billows Replacement Fan Adapter (Single)
Third, the Signals needs to recognize that a Billows is attached. Here, hopefully it actually detects the fan adapter. Can anyone who has a Billows play with this? Does Signals "see" a Billows attached when the fan adapter is attached, but the Billows itself is not?
I'm not hopeful here. Many devices can tell when a USB cable is successful. We're talking a ten cent circuit, to insure that the Signals handshakes with the Billows via the adapter. If they engineered this way, then we can't swap in our fan of choice. If the handshaking is only with the adapter, then swapping in our fan of choice will be easy.
The PID mechanism doesn't care, it sees a black box.