Inside WinPicProg software, you can configure which version of P16PRO40 hardware is being used.
I don't quite catch what you mean by "I have an 74S06N". The following checks assume the one you have bought from eBay has a 74S06N on it.
You can access the menu via "Options>>Hardware" and then "Programmer Types" and select P16PRO40-7406 as your choice. Then all your LEDs except the power green LED will be off.
If that is not the case, then you can manually invert the LED states via putting a tick in the option at the bottom of the signal as shown.
The desire result is after you have started up WinPicProg, with the parallel cable connected and the P16PRO40 powered up, the two RED LEDs should be off. Then without a PIC in the socket, selects 16F877 in WinPicProg and performs a "READ" operation. The Vpp40 red LED will light up and you can measure +13V at socket pin 1. Also confirm +5V available at socket pin 32. After the READ operation finished, these two voltages will drop to zero. You can perform the READ operation as many times as required to confirm the meter reading. Again, if the desired state comes up inverted, put a tick in the bottom to invert it.
Edited: The two red LEDs marked "Vpp40" and "Program" display the voltage level of Vpp40 and Vpp.