Nobody knows how much battery life is used by any particular operation. There are precious few people with the skills and equipment to test this. The best you get is rough impressions.
For the record, I leave my location services on ALL the time since the last new software release and I charge my battery once per day. In fact, I have pretty much ALL radios enabled all the time, Wifi, Bluetooth, 3G, GPS. Apple seems to have gotten battery management under control (finally).
The GPS is a receive only device. It does not send anything. It does not "ping".
When you power it up the GPS chip already knows about the nearest towers and wifi routers (even wifi you are not connected to). It uses that data in order to get a rough fix on where it is.
If near a Cell tower that broadcasts GPS Almanac info, it knows the times and frequencies to listen for satellites passing overhead. Without these it has to sample many frequencies till it finds a "bird" from which it can download its almanac database of times/frequencies.
Without an Almanac, this process takes more battery, because the process is sort of intense till it gets an almanac built up. Having cell towers nearby helps, they forward almanac info helping the phone know where and when to listen for birds.
But if location services are off, it FIRST has to download the almanac (as well as a rough estimate of its current location relative to the tower) and then it can start its search for satellites. If no cell towers are in range (out in the boonies) it has to fall back to listening for satellites directly. This can take time. 15 minutes sometimes. Lots of battery wasted.
See: How a GPS Receiver Locks for what the phone has to go thru without an almanac.
If you leave it running, it has a constantly updated almanac. That means the GPS chip has to do much less work to find the satellites. It knows precisely when birds will be overhead, and can wake up briefly and update its almanac and its clock with a strong signal even while the phone is in sleep mode, and then go back to sleep, wasting as little battery as possible.
The end result is, (as best as I can tell), leaving the location services on 23/7 seems to take very little battery, so little as to be unmeasurable.
I suspect you will use more battery standing around with the screen lit up waiting for a fix when you need it than you will save by turning location services off.
If you use it once a month, you might be tempted to turn it off and save the battery. But you will STILL have to charge the phone every day, so what's the difference?
Side issues and myths:
The way you worded your question suggest that your concept of a "Ping" is fundamentally flawed. It just listens. If it has an almanac, it does less listening, and less computing. It never sends anything.
Having your GPS on does not make you track-able.
Calling 911 will report your location to the operator if they are equipped to receive it. They will get a rough location with GPS off (based on cell tower triangulation) and a much better fix with GPS on. When you want to get help this is exactly what you want. If you want to make an anonymous report, borrow someone else's phone.