Link is broken, but it also just goes to a marketing site.
Found the manual at
https://greatplainsindustries.com/pages/flomec-owners-manuals-and-instructionsDatasheet available at
https://greatplainsindustries.com/pages/flomec-data-application-sheetsor direct links
https://s3-us-west-2.amazonaws.com/catsy.467/qs100-owners-manual.pdf and
https://s3-us-west-2.amazonaws.com/catsy.467/qs100-data-sheet.pdfNeither give much information, and just say it will work with various irrigation controllers.
I think your problem is just too high a resistance value for the pullup. Keep in mind these are ultrasonic sensors and are powered by the same two wires that carry the pulses. Quiescent current when there are no pulses may be quite low, but active current could be a lot higher.
Assuming a 12V supply and off-state quiescent current of 200uA per datasheet, with 4700 ohms you will see a drop of 1V normally, so Off-state V-high is about 11V. Then for On-state, the current would be 12/4750 = 2.5mA, so On-state V-low should be about 125mV (2.5mA through the internal 50 ohms). If it is working, those should easily be seen on a scope. The pulses should go low for 4ms, and repeat at a rate dependent on flow up to 100Hz.
If you are not seeing something, then you should try a smaller value resistor. I've seen similar sensors that require a minimum of 10's of mA to operate (100's of mA on bigger ones), although many recent models are happy running off 4-20mA current loops.
With a 1k pullup, Off-state V-drop would be just 200mV, so Off-state V-high of 11.8V, and On-state current would be about 11.4mA, so On-state V-low about 570mV. I'd even try going lower, maybe 470 ohms.