Remember, I told you that I will let you know when I find out what's going on myself.

[B45]

Said on the phone during real time:

Remember, I told you that I will let you know when I find out what's going on myself.

VS

Remember, I told you that I would let you know when I find out what was going on myself.

Are both okay here? Which would a native use?

 

[MikeNewYork]

They are both OK.

In the first, something is still going on; in the second something was going on in the past.

 

[Raymott]

They're both OK and, where I come from, the second could be still going on, since it's back shifted to past tense to comply with the rest of the sentence.
It would have to refer to the past if it said: "I'm telling you that I will let you know when I find out what was going on myself."