Timing belt change concern...

Hello to all.

I just broke the camshaft bolts free on my 03 3.4 tacoma. I do not believe the cam seals were changed at my first belt change 100K, so I figured Id buy the aircabin man kit and deal with it now(196K).
This is for sure the most delving I have done into any engine mechanics...ever. But that was the whole Idea, to actually learn a bit and learn from my mistakes, which it's possible I'm in the middle of one now.
The left cam socket I managed to keep in the TDC position. The right camshaft for some reason when the cam holding tool was put on the cam(and a little tension was applied, basically just getting the tool into the slots and locking it against the slots), the cam made a snap/click sound and rotated to about the 2 o'clock position. I haven't removed the cam bolt completely as I am not sure that I wont totally lose a way to find TDC??
My question is, should I rotate this right cam by itself clockwise back to TDC before I remove the nut? Or will that somehow interfere with the positioning of other engine components as I turn it? Or should I turn it counter clockwise. I have read not to turn the engine counter clockwise, but is this specifically referencing the crankshaft or the crank and camshafts? It was a little surprising to see/hear the cam jump like it did.
Another question I have is that with the cam nuts loose, both cams rock to and fro a bit, 1/8" clockwise and counterclockwise. Does this somehow mess with getting the cams back exactly in TDC or will the cams settle into the correct spot upon tightening.
Ive included a photo.

Thank you all for your help.

P.S.
Since Ive got your attention, on the right cam there is a square piece protruding 180 degrees opposite the TDC mark. On this square piece there is a white paint mark too. Is this some kind of cruel joke from the factory to confuse aspiring mechanics such as myself?
I love this truck.

 

The white marks are where the "key" is on the camshaft. There will also be a a mark on the crankshaft pulley for top dead center. Match them all up & you'll be good to go. The cam pulley on the left is off.

 

The cam gears will rotate a little when the bolts are loose, pay attention to the dowel pins used for alignment, they don’t always fit tight and I have had them fall out (20min search under the truck) when you set the gears back on turn the gears clockwise against the pin then tighten the bolts, this keeps the cams better in sync and is slight timing retard in cam timing but it seems to run better and smoother ( my experience) liken it to “degreeing” the cams done in racing engines more accurately setting timing between cam and crank more accurately.

The new timing belt will (should) have alignment stripes for all timing locations to help with getting things set correctly. Once installed and you rotate the whole assembly they will not line up with the marks again for several revolutions, as long as the permanent marks on gears do every other evolution, you’re good.

the 3.4 is a NON interference engine, you can turn the cams or crank with no belt and no damage will occur.

the square protrusion on the right side gear is a timing reference for the ECM, the sensor you pulled off (hanging in the pic) picks up the sweep as it goes by.

have fun !

 

Yeah, timing belts are a pain. Glad they went back to timing chains. At least it's a non interferece engine, no bent valve stems, etc. Good luck, Kevin

 

Thank you all for the information. I am having some fun as I am learning. I was just worried about banging expensive things within the engine into each other. I think i will upload a video of the engine upon firing it up. But please, dont expect it to be in the next few days......
Thanks for the positive energy from all of you,
Kevin