inferring signature from function for conditional execution

[leaden mortar]

really no way to infer the type of a function?
At runtime? There are no types at runtime.

It's the only function in the union tho, so you could do if (typeof this.rule === 'function') {}

TS will ensure the signature is correct. If you need to handle multiple different types of functions then you'll need a way to differentiate them at runtime, you'll need to implement it yourself.

Generally speaking btw, accepting a bunch of wildly different types at the same time gives me code smell.

In your case instead of the chain of ifs you may want to consider subclassing instead.