Engineering is like it's own union. Once you have a seat at the table- You are set for a decent career barring any mistakes.
The EO can determine how much he wants to/can afford to fly. My last EO was a primary IP for the unit and flew the lion share of the test flights, plus standing a regular duty rotation. The new EO is not yet an IP, but flies a lot of test flights and stands duty.
Our AEO is an IP for the unit and flies a fair bit.
Larger and/or special purpose units (Atlantic CIty, Elizabeth City, ATC Mobile, HITRON, any Dual Airframe station) I see the potential that the EO/AEO flying less due to the increased work load and special missions requirements.
The following is personal opinion and should not be construed as "good advice" or "the way"...I've got some great input from a lot of folks on it and I have my own opinions. Just putting it out there.
As far as getting a XO tour- I would not recommend it. That's 4 years of developing one skill set @ 20kts...and then starting over learning new stuff at 120kts.
It also puts you up against some time constraints for promotion. 2 years first tour, 2 years XO tour, 2 years (or so) flight school. So you show up at the Air Sta as a LT copilot. So then you need to qualify in the aircraft(~1.5-2 years), and hope to get a dept head job in that same time so your OERs are set to compete for LCDR. Not to say it's NOT doable...It's just more work and it can short you out of flying down the line (staff tours, grad school etc) and put you behind your classmates in terms of qualification (You'll see guys as second tour AC's while you are a CP).