Here's my setup:
I'm trying to emulate the circuit to the right with the one on the left. That is, the one on the right is a pre-charged capacitor (node3) being discharged to its capacitor pair via a resistor (at this point, I'm asking about \$I_{max}\$ of the equation $$I(t) = I_{max} e^{-t/RC}$$.
The experiment on the left has the same setup, only it's an Arbitrary Behavioral Current Source, instead of a resistor, and it's not working as the one on the right.
What's wrong?
Your title is as much of an XY problem as it can be. What you want is an emulated resistor, not a specific help about behavioural sources. Your expectations are also wrong: a resistor is not a current source. But if you want a resistor to be emulated by a current source then you need to apply Ohm's law: I=V/R -- currently, you discarded V and only used R (or an attempt at 1/R). So, to correct the problem, you have to use V in the equation, and it can be done in two ways:
B1's expression is V(a,b)/1k, where V(a,b) is V and 1k is R (considering R1 from your circuit). G1 is a 4-terminal element, whose two inputs are connected across the output, forming V(a,c), which is the V. Its value is 1m which is 1/1k. The two behavioural sources below show the equivalent value of the two emulated resistors (green labels) -- they are 1 kΩ, both.
