For us, we had the $1K then rolled it into the 3-6 months when we got to that step

Our retirement is totally separate. The FFEF is split between 2 banks, passbook savings at one bank and a regular checking at our “main” bank where more of our accounts are. We can write as many checks as we want to with no penalty and no minimum balance on the savings or checking.

The retirement is made up of traditional IRAs utilizing mutual funds for dh and for me. We max them out each year. But that does not put us at 15% so we are investing in non-retirement accounts using mutual funds. We have never taken anything out of any of these mutual funds (retirement or non-retirement). That is what the FFEF is for.

I am not so sure it matters where the money is parked

It matters that the money for both funds, is available. At some point the BEF will become part of your larger Emergency fund and all of that will roll over into retirement or general savings as you get further and further away from debt.
I wouldn’t stress on having multiple accounts as much as I would be concerned that I have money set aside in case something drastic occurs.