Flashing text is a feature of the video hardware, and on early Apple II models the cursor is just a space character with the Flash bit enabled.
You can turn on flashing text with the FLASH command. E.g.:
FLASH:?"HELLO WORLD"
Later models will produce the flashing cursor in software rather than hardware, so you can't inadvertently end up with multiple flashing cursors on screen.
No worries. I am actually into the machines at the moment, so a lot of it is spooled up, reasonably fresh.
The blink implementation will work when video does. Pretty much independent of CPU state. That whole circuit works on phase 2 of the 6502 bus clock and is basically transparent to the CPU.
That kind of thing normally takes wait cycles, or multi port RAM.
Bonus points: Doubles as RAM refresh.
The only impact is a slightly longer cycle every 63 (I think) cycles to make the video line up with the clock to allow for the artifact color hack to work consistently.
To the CPU, there are no waits and it runs at full speed. In physical time, that long cycle takes a bit longer than the other ones which can complicate things like bit banging audio, if not done on a long cycle multiple.
Having come from that era, watching this play out was interesting.
The Apple was simple, very practical. Other more complicated and advanced machines had custom silicon. Sound, graphics.
But, they often lacked utility, and the outcome was Apples being workstations.
A whole lot of code and hardware dev for other systems got done on Apples, which offered enough of the basics to cover most bases.
80 columns, fast disks, slots, easy interfacing, no interrupts or DMA in base system, 6 color graphics not just 4, etc...
The set of tradeoffs is admirable.
I use mine today for retro code tinkering and some hardware fun. I have it running at 16Mhz, (which frankly is stupid fast) with the 16bit 65816 in it just for kicks. And that is robust. I can turn a knob and dial the clock up or down never missing a beat. Weird and fun.
Bonus: Grand kids can experience Oregon Trail.
I jumped onto one of these in the 80's and learned a ton!