Clearing up a couple of steps, via actual tests on my Z6:
(when testing this, I set up the options, but hey, it didn't wait 2 seconds to start. Oh, of course--I have to press the Release Mode button and switch to Self Timer!)
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Bracketing shows on the display as "AE bkt" and "3/3" three shots to go of the set of three. It counts down 2/3 and 1/3, Then back to 3/3 for a new set.
One photo per shutter press in Single shot mode, counting down.
Or the whole set, then stop, with holding down one shutter press in any continuous mode (and there's no delay between exposures).
Or the whole set on one button press with the starting delay and between shots delays, in Self Timer mode.
c2 Self Timer:
Self timer delay = 2s
Number of shots = 1 (This only applies to using the self timer without bracketing. for example, 10 s delay, take 3 shots...a good "selfie" mode. In bracketing mode, it always shoots one image per bracket step.)
interval between shots = 0.5s, 1s, 2s, 3s. I used 1s. Does the Z8 allow a shorter interval than 1/2 second? the online manual page doesn't say. That's not useful for non-bracketing self timer shots, of course, so it probably doesn't allow "0 s".
Bracketing:
The bracketing settings are on menu button--> Photo Shooting menu.. Scroll way down to Auto Bracketing.
types of bracketing: AE &flash, AE, flash, WB white balance, or ADL--Active D lighting Off or various values, depending on number of shots. I've only used "AE".
Number of shots: 0 (off) to 9
Increment: 0.3 to 3 stops (for AE bracketing)
at 1/3 EV, the Number of Shots choices are:
Code, shots, shot sequence (for MTR>under>over).
0F, 0, 0
+3F, 3, 0/+0.3/+0.7
−3F, 3, 0/–0.7/–0.3
+2F, 2, 0/+0.3
−2F, 2, 0/–0.3
3F, 3, 0/–0.3/+0.3
5F, 5, 0/–0.7/–0.3/+0.3/+0.7
7F, 7, 0/–1.0/–0.7/–0.3/+0.3/+0.7/+1.0
9F, 9, 0/–1.3/–1.0/–0.7/–0.3/+0.3/+0.7/+1.0/+1.3
"for exposure increments of 2 EV or more, the maximum number of shots is 5."
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I use the i-menu version of this Photo Shooting-->Auto Bracketing, with the same options, but fewer text prompts on screen.
And I have the c2 Self Timer and d4 Exposure delay mode next to each other on the first page of My Menu, with the red video button launching My Menu.
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Other bracketing related settings:
menu --> e bracketing/flast menu --> e6 auto bracketing (mode M) has 4 choices: flash/speed, flash/speed/aperture, flash/aperture, flash only. I've never used these.
and
e7 Bracketing order I like the shots taken in Under >MTR(meter)>over, instead of MTR > under > over. The exposures are in sequence when I review in my photo editor. Either way, the final image of the sequence is shown first when pressing Image Review on the camera, which for 3F is the "over" exposed one.
Perhaps getting the metered exposure taken first has a small advantage in fast moving scenes -- get the good exposure, then shoot the under and overs.
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Powering off and back on:
The Self Timer release mode reverts back to my usual "S" single shot.
The bracketing doesn't reset, it's still in effect. And self timer settings never change, of course, since it's controlled by the Release Mode.