NVeater and Daz,
Welcome to owning a Cummins 6BTA. They are great engines (with a couple of weaknesses) and will give many thousand of hours of service if well maintained.
Do yourself a big favour and go to sbmar.com (Seaboard Marine's website) owned by Tony Athens, a marine diesel guru, especially all things Cummins.
Yes, it is a commercial site where he sells products and services, but he gives freely of his vast knowledge accumulated over 30 plus years of experience, both with answers to questions on his forums, but with tons of articles under "Tony's Tips".
Your photos show an engine that "looks" like it has been looked after.
Potential issues to consider addressing on this engine include:
1) Idle pulley bolt replacement.
2) Replacing the Sherwood raw water pump with a much better (but same or cheaper priced) pump from Seaboard.
3) Replacing the Walker Airsep with a better CCV system, especially if your turbo shows signs of oily buildup.
4) Installing a freshwater flush system. See articles about "Marine Age".
5) If still using the stock Cummins (white double jacketed exhaust), changing that out to a custom exhaust (see the article on sentoa.org under tips "Cummins wet exhaust issues on early NT37 by Kelly Britz). This one is very important.
6) Regularly service your Aftercooler(s). Every 3 years or so, unless freshwater flushing then maybe every 4-5 years.
You have received a good answer for the "red button".
Enjoy your great engine.