Fear not avid readers! The OldSpark has rekindled the old 555 circuit's (brain) cells....
(Thank you KP - I am honoured!)
Increasing the voltage to 12V:
I agree - increase cap rating to 25V (or higher). (It's recommended to have a good voltage rating margin.)
And relays to 12V.
The LED's 330R resistor can probably stay as is PROVIDED it is rated for 1/2W - it'll just be brighter - but 820 Ohms would be its equivalent 12V value, else anything in between. (820R 1/4W is fine, but stick to 1/2W - traditionally they were considered robust etc.)
Similarly the BC107/148's 22k to 33k - but that's probably insignificant since it's merely acting as a signal inverter (no load) and well withing its capabilities.
The timing will not change - it's an RC time constant where all voltages are proportional to the supply voltage (ie, RC voltage and the 555's comparator voltages - FYI: which are 1/3 & 2/3 of the supply voltage).
The 555 can source and sink
200mA.
At 12V, V=IR hence R=V/I = 12/.2 = 60 Ohms.
Hence it should drive relays with solenoid resistance HIGHER than 60R (I use R as shorthand for Ohm instead of the Omega symbol).
BUT!!! - if by 12V you mean "vehicle", that could be 14.4V, though I will usually design for 16V.
The same V/I = 16/.2 = 80R.
Why did I do that? Because many automotive 12V relays are ~68 Ohm and hence a borderline case. (There are reasons why they usually are ok, but is it worth risking?)
But I like transistors for the heavier outputs - they buffer the 555, are cheaper to replace etc, though is is another point of failure....
IMPORTANT!! None of your circuits show "decoupling capacitors". These are merely 0.1uF caps across the power supply to snub transients - especially in the triple 555 circuit (TT5 = triple triple-5 circuit?).
Place a 0.1uF cap across each 555's pins 1 & 8 and as close as possible to them.
The 555 can generate a big switching transient which can unintentionally trigger other circuits an 555s.
Often a larger cap may be used across the supply as well (1uF or 10uF electrolytic cap with 25V rating) bu that would accompany other protecting in automotive circuits (zenor/voltage protection, series resistor etc) but wouldn't be required from a clean power source with adequate cabling.
How'z that for a dusty old brain?
My last 555 build was.... not in this millennium.
Though a few years ago I got the components for a wiper delay and a headlamp dimmer for my ute (pick-up), and a camping 12V fluoro-lamp dimmer.... Can't rush these things you know.
Besides, for some reason I keep getting distracted...
BTW - It's bad if you don't get replies - unless you have posted bad eksprzion, though I will often skip non-informative topic headings/subjects.
Otherwise a bump may be worthwhile (certainly after a few days).
The best thing though is getting the good replies - like CK & KP above. (If CK hadn't have detailed all that, I would have missed most details. It may have been a shorter answer, but maybe your 330R would have smoked, and your tt5 circuit false triggered.)