My Raymarine autopilot is interfaced with my PC running Coastal Explorer, it's also connected to my Furuno NavNet. I'm a professed geek, I get a great deal of satisfaction in getting things to work when the "conventional wisdom" says "oh, you can't do that....". "Uh, yes, I can...."
Your ST6001 is the control head, it connects to the course computer, the "brain" of the AP via SeaTalk, and doesn't know or care about the chartplotter. Its function is the control and a window into the AP. That's all. You don't have a ST6001 autopilot, you have an S2 course computer with a ST6001 control head. Detail point, but the devil is in the details in getting things to play nice. So there's a lot of necessary detail in this epistle.
Connecting the autopilot with your new gear is do-able but you must provide the connections. Note that the Garmin uses the black "ground" wire, typically it's the NMEA (-) on both TX and RX. (That's transmit- e.g. NMEA out of the GPS and into the AP -- and receive - NMEA into the GPS and out of the AP).
Find a cable that has two twisted pairs of stranded wire about 22 ga. in a shielded insulation. The twisted pair makes for cleaner signal. You can also use cat5 or 6 ethernet patch cable (patch is stranded), it's not shielded but it will work fine. The longer the run, the more advantage there is in shielded cable.
Your AP outputs compass heading, and that may be very helpful for your chartplotter if it doesn't have any other compass source. That would be obtained from the NMEA 1 "out" or TX at the AP, and it would connect to the NMEA "in" or RX of the chartplotter. The S2 should have 2 NMEA connections, NMEA 1 has compass data and rudder position out. Each NMEA port should have 4 spring tab connections. Depress the spring tab, insert the wire into the hole next to it. EZPZ. It's often helpful to wear your bifocals upside-down! You'll connect one twisted pair to TX (+) (-), the other to RX (+) (-).
Your Garmin manual should explain the color code of the NMEA pigtail that comes out of the back of the device. You'll need to connect to the corresponding NMEA 1 port of the chartplotter. Likely you'll be connecting both the (-) wires to the black ground wire of the Garmin, they use a common unlike the Raymarine where each conductor connects separately. It is key to observe the correct orientation of (+) and (-), if you cross them, nothing will work. You'll do yourself a huge favor if you use a terminal block
to make the connections. Use a 12 position or appropriate block with #6 screws, crimp a fork terminal on the ends of the wires to make it easier to re-do connections or add new ones. Gear TURNED OFF while wiring, contacting a live 12V conductor with any of the NMEA conductors can be fatal to the NMEA circuits.
Once the connections are complete, you'll need to insure that the chartplotter is sending the needed data to the AP. It requires configuring the NMEA ports on the chartplotter. You'll need to turn on the needed NMEA sentences on the corresponding NMEA "out" port on the chartplotter. You'll need to turn on APB at a minimum, plus RMC, VTG, perhaps XTE although that data is generally included in APB and RMC. Resist the temptation to turn on every sentence, NMEA is slow and has limited bandwidth, less is more.
Your 6001 has the ability to display a variety of data, and that data is coming into the course computer from the chartplotter via the NMEA port. It NEEDS the sentences mentioned above to be able to steer a route from the chartplotter. It CAN display additional data, but that may be unimportant to your use. It's just useful to know that if your control head can display certain data but doesn't, it may be that the chartplotter isn't transmitting that data because the NMEA "out" sentence isn't turned on. If that's something you want, get the basics working then add a sentence at a time.
You can see what data the AP is transmitting to the chartplotter by using the port monitor that should be in the configuration menu of the chartplotter. It will display the NMEA data that's being received. There is no corresponding function on the AP, but the control head will display data. For example, you can toggle through the display screens on the 6001. If you activate a route on the chartplotter and it's connected properly, your 6001 will display waypoint name, distance to waypoint, bearing, etc. Key is to be sure you have the chartplotter activate a route, that triggers the transmission of the data to the AP. That data is coming from the chartplotter. So if a route (or simply a "goto waypoint" is active, the data should be there. Its absence, or NO DATA on the 6001 would indicate that the data isn't getting there, so there's a glitch in the configuration. The 6001 manual will help.
Patience and methodical attention to the details is key to getting the gear to play well, it's not as daunting as it appears, you just need to pay attention to the small stuff, as it doesn't take much to make it go sideways.