How to fake an encoder signal with one function generator?
I would try following approach:  


Set the frequency of the function generator 2 times higher then the desired frequency (so 120Hz if you would like to have 60Hz)  
Build the divider by 2 with quadrature output with 74** logic chips. There are many solutions available, schematic of the one that could work is shown below *). It uses one chip with two D flipflops (for example 74??74) and one 74??86 chip with 4 xor gates (only 2 are used).  




*) I have just drawn it without any simulations or prototyping. It is not guaranteed to work, but you get the idea.