If I contact the trustee of the first and let them know I am the new owner, will they postpone the auction so I can have more time before paying off the first?

Most can't, and without that title search you could up losing your money.There's a possibility the sale could be postponed or withdrawn.

https://www.flsenate.gov/Session/Bill/2019/01128Last Action: 5/3/2019 Senate • Indefinitely postponed and withdrawn from considerationSigh...

Now they are just postponing.

Properties are constantly being removed from the sale list for various reasons - property gets sold before sheriff sale, bankruptcy, postponement as allowed by law, payment arrangement is agreed to, and court order is issued are just some of the more common reasons properties get removed from auction.

Here the Sheriff in 65 of the counties including Berks does not handle tax foreclosure which is conducted by another county agency.From the initial Sheriff Sale list about 1/3 are stayed (cancelled) about 1/3 are postponed, and about 1/3 actually go to sale. 

The practical challenge with paying for this service is that your time frame to obtain the title report is very short, and the list of properties can be long, and to make matters worse most of the properties that you pay to title search don't actually go to auction, they postpone or cancel.I don't mean to sound like a downer on this business--I've made my living in this business for over 20 years--but I've seen too many people who are unprepared for the risks lose their life savings.

(This part is not true in all states.)Alternatively, if the lender will postpone the sale for you, you can buy the property and pay off the loan entirely going through escrow.

The area where I look even has online updates that are very timely - I can see the morning of the sale which ones have already been postponed.

On the other hand,   If they have paid enough to satisfy you, but aren't totally caught up, call the court to get the hearing postponed a month.