I believe I got the flows working, but as a newbie I'd love some criticism so I can learn if there are better ways to do it. I feel like this was very 'round about'.
[{"id":"dc46be20.8e86","type":"tab","label":"Sprinkler vs Mower!","disabled":false,"info":""},{"id":"896c9eb1.df30e","type":"switch","z":"dc46be20.8e86","name":"","property":"payload","propertyType":"msg","rules":[{"t":"eq","v":"Cutting","vt":"str"},{"t":"eq","v":"Cutting (manual timer override)","vt":"str"},{"t":"eq","v":"Going to charging station","vt":"str"},{"t":"eq","v":"Leaving charging station","vt":"str"},{"t":"eq","v":"Stopped but not on base","vt":"str"},{"t":"eq","v":"Paused","vt":"str"},{"t":"eq","v":"Charging","vt":"str"},{"t":"cont","v":"Parked","vt":"str"}],"checkall":"true","repair":false,"outputs":8,"x":90,"y":640,"wires":[["452d1da4.5a4194"],["452d1da4.5a4194"],["452d1da4.5a4194"],["452d1da4.5a4194"],["452d1da4.5a4194"],["452d1da4.5a4194"],["85d07afd.a07c38"],["85d07afd.a07c38"]]},{"id":"452d1da4.5a4194","type":"change","z":"dc46be20.8e86","name":"Set ON","rules":[{"t":"set","p":"payload","pt":"msg","to":"on","tot":"str"},{"t":"set","p":"topic","pt":"msg","to":"mower_status","tot":"str"}],"action":"","property":"","from":"","to":"","reg":false,"x":240,"y":620,"wires":[["6ef232fa.16511c"]]},{"id":"85d07afd.a07c38","type":"change","z":"dc46be20.8e86","name":"Set OFF","rules":[{"t":"set","p":"payload","pt":"msg","to":"off","tot":"str"},{"t":"set","p":"topic","pt":"msg","to":"mower_status","tot":"str"}],"action":"","property":"","from":"","to":"","reg":false,"x":240,"y":660,"wires":[["6ef232fa.16511c"]]},{"id":"cae42b7e.94a3d8","type":"server-state-changed","z":"dc46be20.8e86","name":"Mower ","server":"9344209b.b3b01","version":1,"exposeToHomeAssistant":false,"haConfig":[{"property":"name","value":""},{"property":"icon","value":""}],"entityidfilter":"vacuum.robi","entityidfiltertype":"exact","outputinitially":true,"state_type":"str","haltifstate":"","halt_if_type":"str","halt_if_compare":"is","outputs":1,"output_only_on_state_change":true,"x":90,"y":740,"wires":[["896c9eb1.df30e"]]},{"id":"f04be0bc.9601","type":"api-call-service","z":"dc46be20.8e86","name":"Turn off Skydrop","server":"9344209b.b3b01","version":1,"debugenabled":false,"service_domain":"switch","service":"turn_off","entityId":"group.sprinklers","data":"","dataType":"json","mergecontext":"","output_location":"","output_location_type":"none","mustacheAltTags":false,"x":670,"y":100,"wires":[["3c2583ef.838bec"]]},{"id":"b6c312ca.754b2","type":"join","z":"dc46be20.8e86","name":"","mode":"custom","build":"object","property":"payload","propertyType":"msg","key":"topic","joiner":"\\n","joinerType":"str","accumulate":true,"timeout":"","count":"2","reduceRight":false,"reduceExp":"","reduceInit":"","reduceInitType":"","reduceFixup":"","x":430,"y":200,"wires":[["5e2ef6a4.af3698"]]},{"id":"63e91f91.c9932","type":"server-state-changed","z":"dc46be20.8e86","name":"Sprinkler Group","server":"9344209b.b3b01","version":1,"exposeToHomeAssistant":false,"haConfig":[{"property":"name","value":""},{"property":"icon","value":""}],"entityidfilter":"group.sprinklers","entityidfiltertype":"exact","outputinitially":true,"state_type":"str","haltifstate":"","halt_if_type":"str","halt_if_compare":"is","outputs":1,"output_only_on_state_change":true,"x":100,"y":200,"wires":[["523d0a6d.856be4"]]},{"id":"c3447a2c.0fe768","type":"ha-entity","z":"dc46be20.8e86","name":"Mower Sensor","server":"9344209b.b3b01","version":1,"debugenabled":true,"outputs":1,"entityType":"sensor","config":[{"property":"name","value":"mower_state"},{"property":"device_class","value":""},{"property":"icon","value":""},{"property":"unit_of_measurement","value":""}],"state":"payload","stateType":"msg","attributes":[],"resend":true,"outputLocation":"","outputLocationType":"none","inputOverride":"allow","x":100,"y":260,"wires":[["b6c312ca.754b2"]]},{"id":"523d0a6d.856be4","type":"switch","z":"dc46be20.8e86","name":"","property":"payload","propertyType":"msg","rules":[{"t":"eq","v":"on","vt":"str"},{"t":"eq","v":"off","vt":"str"}],"checkall":"true","repair":false,"outputs":2,"x":260,"y":200,"wires":[["846771eb.3dc41"],[]]},{"id":"6f198be7.1e7c74","type":"debug","z":"dc46be20.8e86","name":"","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"false","statusVal":"","statusType":"auto","x":710,"y":400,"wires":[]},{"id":"84e30133.8df8d","type":"inject","z":"dc46be20.8e86","name":"","props":[{"p":"payload"},{"p":"topic","vt":"str"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"","payload":"on","payloadType":"str","x":170,"y":120,"wires":[["523d0a6d.856be4"]]},{"id":"6ef232fa.16511c","type":"delay","z":"dc46be20.8e86","name":"","pauseType":"delay","timeout":"1","timeoutUnits":"seconds","rate":"1","nbRateUnits":"1","rateUnits":"second","randomFirst":"1","randomLast":"5","randomUnits":"seconds","drop":false,"x":160,"y":420,"wires":[["c3447a2c.0fe768"]]},{"id":"846771eb.3dc41","type":"change","z":"dc46be20.8e86","name":"","rules":[{"t":"set","p":"topic","pt":"msg","to":"sprinkler_status","tot":"str"}],"action":"","property":"","from":"","to":"","reg":false,"x":410,"y":140,"wires":[["b6c312ca.754b2"]]},{"id":"5e2ef6a4.af3698","type":"function","z":"dc46be20.8e86","name":"","func":"if (msg.payload.sprinkler_status === \"on\" && msg.payload.mower_status === \"on\" ) {\n msg.payload = \"on\";\n} else {\n msg.payload = \"off\";\n}\nreturn msg;","outputs":1,"noerr":0,"initialize":"","finalize":"","x":560,"y":200,"wires":[["1709426e.3dcfce","6f198be7.1e7c74"]]},{"id":"1709426e.3dcfce","type":"switch","z":"dc46be20.8e86","name":"","property":"payload","propertyType":"msg","rules":[{"t":"eq","v":"on","vt":"str"},{"t":"eq","v":"off","vt":"str"}],"checkall":"true","repair":false,"outputs":2,"x":690,"y":200,"wires":[["f04be0bc.9601"],[]]},{"id":"3c2583ef.838bec","type":"api-call-service","z":"dc46be20.8e86","name":"logbook.log","server":"9344209b.b3b01","version":1,"debugenabled":false,"service_domain":"logbook","service":"log","entityId":"","data":"{\"name\": \"NODE RED Triggered\", \"MOWER vs SPRINKLERS!\"}","dataType":"json","mergecontext":"","output_location":"","output_location_type":"none","mustacheAltTags":false,"x":870,"y":100,"wires":[[]]},{"id":"9344209b.b3b01","type":"server","z":"","name":"Home Assistant [Bromley]","legacy":false,"addon":true,"rejectUnauthorizedCerts":true,"ha_boolean":"y|yes|true|on|home|open","connectionDelay":true,"cacheJson":true}]