I would do what others have recommended. Take vacation and come into the current employing agency for one last day to check out. Or, check in to the new agency (attend orientation, etc.) and then take annual leave before really starting the job. It depends on the employer as to which is more likely to say ok to the arrangement. But, because mistakes happen, you are probably best being cautious to ensure no break in service occurs through a paperwork snafu.

When I changed agencies I gave 6 weeks notice and then took 4 weeks LWOP. I did have to be physically present on my last day to turn in my laptop and PIV card (they wouldn't offboard me first). You need your supervisor to support you in getting everything correct for HR.

You can’t. I tried. I honestly just needed an unpaid break between jobs and was told no. I was only getting 4 hours a pay period and just needed a break.

I’d just lie and say I need to take four to six weeks to care for a sick relative and that you’ll use annual leave instead of FMLA.

Then return after four to six weeks and quit. Give 2 weeks notice.