Note – While this Post documents my IC-7600 setup, I believe this will work equally well with the IC-7610 but I do not have one to test. If anyone can provide confirmation or feedback, it would be appreciated.
I have had the IC-7600 for about 4 years and have now added the Elecraft KAT-500 Antenna Tuner and the KPA-500 Amplifier to the setup. Using the Elecraft “Power Combo” (as they call it) with Icom radios, has been the subject of several Blog posts here and the topic of discussion with many other Hams. After a couple years of trial and error (some fairly significant!), I have now settled on a wiring arrangement that seems to work very well and also makes me comfortable.
The minimum necessary wiring can be debated. Some say you only need to connect the RF and off you go. The Elecraft KAT/KPA-500 can recognize the RF frequency and adjust everything for a match, if your antenna is within the range of match for the KAT-500 Tuner. At the very least, you want to add an INHIBIT line from the Tuner to the Amp, which allows the Tuner to quickly Stop transmission if anything goes awry.
The attached diagram shows my final wiring arrangement that includes a couple options I would not operate this setup without. Number one is the addition of the AH-4 Tuner connection from the IC-7600 to the KAT-500 Tuner. While I have heard debate about the use of this connection, it works great for me. The downside is that the KAT-500 claims that ~ 25 Watts are required for proper Tuning. However I read a Lab Report on the Tuner that said it seemed to work equally well with ~ 10 Watts, which is what the IC-7600 provides while Tuning. Elecraft has told at least one person that they do not recommend using this connection due to the power-level issue. I respectfully disagree with that.
The other wiring option is the addition of a BAND Data connection from the AUX2 port on the IC-7600 to the AUX1 connector on the KPA-500/ This cable is documented in the KP-500 manual. It allows the Amp to follow Band changes on the Radio. This makes me more comfortable, and I believe it has saved me many times from a “Fault” when quickly changing Bands.
This setup has worked quite well for me over the past year or so. I would be interested in any feedback or comments or improvements you may suggest.
Kg3v Ham Radio Blog 
Where did you get the cable to connect the round ACC2 on the 7600 to AUX 1 on the KPA? After making this connection, what radio type did you select in the menu on the KPA?
I built a custom cable for the Band Data connection. The KPA needs to be configured to expect ICOM Band Data
Can I pay you to build one for me? I’m always forgetting to change bands.
I am tied up with some things for the next week or two, but after that I might be able to help. I do not want to get into the business of building cables, because it is just not much fun and I can’t test them unless they are for a radio that I own. But if you can’t do it and really want me to, please contact me by email at mycall@arrl.net (replacing “mycall” with KG3V). Be sure to let me know which radio. I think the 7600 and 7610 ACC connectors might be the same, but need to check the manuals.