I also need one of the pulses output to be 10V.
The Arduino can't do that. At best it can turn a transistor on or off, where that transistor controls a 10V source.
to be activated by the counter which will have a cycle of every 8 seconds
This makes no sense to me. Something might be generating an interrupt every 8 seconds, and you might be counting those interrupts, but nothing magically counts something every 8 seconds.
To generate each pulse, would building an array for each square pulse be the best method?
No. Turning two pins on and off at defined intervals after an event requires nothing more complicated than a state machine (waiting to start, waiting to turn first pin on, waiting to turn 1st pin off and second pin on, etc.) and the use of millis() to determine when it is time to change to the next state. When it is, perform some actions and set the time the last state change happened. On each pass through loop(), see if it's time to transition to the next state.
How can I configure a counter to activate every 8 seconds?
Counters count. They don't "activate". You need some kind of timer-based interrupt. Hit google.