What switch and relay circuitry is required to manage two water well pumps effectively?
This can be solved with four special purpose relays.  Relays are basically electrically operated switches.  Alternating relays are special relays that cycle between two or more loads sequentially when they are electrically activated.  

You could cascade one triplex alternating relay with three regular (duplex) alternating relays to achieve what you want - calling pump #1 every sixth call.  

The pressure switch that calls the pump would energize the coil of the triplex alternating relay.  Each of the three outputs of the alternating relay would go to a duplex alternating relay.  

Each of the three duplex relays has two outputs for a total of six outputs.  You'd wire one of the outputs to start pump #1, the rest all to start pump #2.  This is what would be energized each consecutive call for water from the pressure switch-

First call:
Output 1 of triplex, Output 1 of duplex A 

Second call:
Output 2 of triplex, Output 1 of duplex B 

Third  call:
Output 3 of triplex, Output 1 of duplex C

Fourth call:
Output 1 of triplex, Output 2 of duplex A 

Fifth call:
Output 2 of triplex, Output 2 of duplex B 

Sixth  call:
Output 3 of triplex, Output 2 of duplex C

and at that point the cycle repeats.  So if Pump #1 is connected to say Output 2 of Duplex C, and Pump #2 is wired to the rest, Pump #1 will run every sixth call.  

See Macromatic ARP and ATP models for an example.  This may be $300.00 or so of relays - a PLC would actually be cheaper.  The relays would be very simple.  

Then again if you change your mind and you want pump #1 to run 1/7th of the time, with the PLC that's an easy programming change, with the relays you are S. O. L.  



*Original answer...


  I am assuming you have a "flip flop" relay or alternating relay
  currently wired to alternate pump 1 and pump 2.   If there was such a
  thing as a six way alternating relay, that would be perfect for you,
  that might work - you could connect five sets of contacts to pump 1
  and one set to pump 2.  But I don't think such a relay is available.
  
  The best solution is probably a programmable relay, available from a
  variety of vendors, or a small PLC.  However there is some learning
  curve involved with either of these options.*