As soon as you have the Employment Pass Eligibility Certificate (EPEC). You can now apply for a Long Term Visit Pass (LTVP), given that you have entered Singapore with a valid Visa and stayed minimum of 10 days.
I wasn't able to activate my EPEC or apply for a LTVP because I was lucky to get a job in 4 days. My employer applied the Employment Pass for me. So, I am still holding my EPEC copy until now.
Since my reader, Mark, asked me on how to apply for the LTVP, I have done few research on this and was lucky enough to have the links.
How To Apply for a LTVP?
This is also known as "Converting EPEC to a Long Term Visit Pass", in forums. You can click the link below for the detailed procedures: