ILR in old passport, BRP application time frame question

I've searched BRP and see that it usually takes about 2 months to get a BRP. My first question is, do they keep my passports, the old one with my ILR and my new one, the whole time?  I've been here 10 years, first on a fiance visa, then marriage visa and currently on an ILR. I've not even thought about a BRP, as it isn't needed to travel, and I've been self-employed. But I have a trip to the States coming up for Christmas, and have just had a job interview. Is there another way to show eligibility to work? Does anyone know anything about the new service that began 2 Nov '18?

Thanks

Unfortunately you have to have the BRP in order to show eligibility for work, Its been like this for a while.
Well  if you have the old style pink ILR  sticker it woudl still be ok -- you do nto need a BRP per se -- but they have this stupid requirement now that the passport that contains it needs to be current.
This was a sort of blunder when the whole hostile environment was introduced -- well, I call it a blunder, but in reality it was an excuse to get money from more and more people, of course.  Those people they otherwise already had nothing else to milk for.
You just did not have to deal with it. You should not have a problem returning from the trip, if a newbie IO tries to stamp you in as a visitor call the  SIO, do NOT leave the counter if you get the six months visitor stamp in error!
You have to file an NTL application (you get a BRP that says "no time limit" on it.)
Unfortunately these take forever, I have heard of them being stuck for months so do not advise making those by post.
While your case sounds simple unfortunately especially now in the wake of Windrush and such like,  a lot of NTLs are filed by folks with ages-old or nonexistent claims to ILR, so usually this is a long queue.
It used to be possible to do it at the PSC for 600 quid but unfortunately now I have no idea what to do with all the Sopra Steria business.
But I'd not send the NTL appllication by post with any sort of intention to travel any time soon..
 

This was a really long winded way to say that you need a BRP for proof of Right to Work.

You will be without your passport during the application process.

Alternatively, have you considered applying for citizenship instead?