Bert is correct
to elaborate
if you turn the key to the run position, certain circuits are now potentially live with battery voltage. this could head lights, electric clutch battery ignition. when you turn the key to the start position, the previous circuits are active as well as the start circuit.
if the fuse blows when the key is in run, you to check all wires coming out of the switch to the various loads. if it only blows when in the start position, then you can eliminate all of the other circuits and concentrate only on the start. you should have a schematic/drawing and follow the wires. do not jump around as you will miss something.
If you are going to keep this mower I strongly recommend buying the JD manual.
It is written in a mannar that people who do not know which end of a screwdriver you hold can tackle every job.
Very easy to follow and step by step instructions.
Shows exactly where every part you need to test is located , what position the controls need to be in , where to test the wires and most important, what order to do the testing.
Read it carefully and you will be a better mower electrician than 50 % of the techs in workshops now days.
.
Should you sell the mower including the manual will add substantial value to your mower.
Something I found out by accident,if I include operators & parts & service manuals with used mowers sold on evilbay I get more bidding but not much higher price.
However if I include operators, parts & service manuals I get near double the price.
So a $ 60 book that any one could buy adds up to $ 500 to the sale price.