Nice capture - was able to make a 'ruler' (see image).
Interesting that the long pulse are 2.5 times the length of the short pulses. You will need to make quite a few captures, with different buttons pushed/commands, to see what is going on.
Given the slow speed it should be possible to generate that signal with an Arduino, using digitalWrite() and delayMicroseconds(), at least enough to prove the concept.
You might need to do a little more investigation, to see if the signal line has a pullup on it, or who is pulling it up. If it has a pullup on it, you set the pin to zero with DigitalWrite(x,LOW), and then use "pinMode(x,OUTPUT)" to drive the signal low, then "pinMode(x, INPUT)" to allow it to be pulled back up.