My 1998 explorer runs great, starts right up in the morning.

However, after driving for awhile then turning it off and trying to start back up, all I get is some clicking under the dashboard, as if the starter has been disconnected. All lights work, etc....

After turning the key off-on-start off-on-start several times (sometimes minutes of doing this) the current will finally make it to the starter and the engine fires right off.

Seems to be a bad relay or neutral safety switch going bad? Anyone had this problem?

 

I would start with cleaning the battery terminals and connectors. Bad/poor surface contact in this area will causes your symptoms. Expansion and contraction of the contact area can cause poor connection for the high amp draw that the starter requires. Use dielectrical grease after cleaning the posts and inside of the terminal connectors.

 

Battery terminals are clean....and it's a new battery....

What would you check next?

 

Few other things to check. Was there any corrosion on the positive connector going down into the cable casing? If so, this can cause high resistance and low voltage to the starter. Check for corroded connections at the starter. Could also be starter relay, solenoid, or the starter thrust washer casuing poor contact.