Modern Vespa

Lite comes on with acceleration then go's off, stays off most of the time while rolling but comes on during heavy acceleration ie: passing, then go's out, not on at idle. Head lite and dash lites dim and then return to full brightness but head-lite dimms to 30% or less output. intermittent.

oil with in limits
coolant with in limits

check voltage at battery- idle 9.9 volt dc
at speed ( no tach so I made guess as to rpm) 3500+ highest voltage 11.82 volts dc.

I do not belive this to be a voltage reg problem but a charging system problem.

The battery may have been damaged by a bad voltage regulator and that's why you're getting such low readings.
Take the battery to a shop and have them do a load test. If the battery is okay, then you may have a bad stator. If the battery is not okay, you need to replace the battery and test the voltages again with the engine idling and again with it revving. Then, if it goes over around 14.8 volts while it's revving, it's the VR. I used to have a 2007 BV500 and my VR became defective and I've read of at least a half dozen more that have posted on MV with the same symptoms and they turned out to also have defective voltage regulators. Good luck with finding the problem quickly.

I confirm what he has said XLR8
Control the recharge of battery by an external device then
if the battery is ok you can put the battery on the Beverly,
Normal voltage without current consuption is 12,2-12,5V,
Start the engine and control the voltage in various situations,
at minimum rpm (about 1500rpm) voltage must be 13,3V no less,
increase engine rpm and at the medium and high rpm the voltage
dosn't go over 14V, if voltage is over 14-15-16V the recharge regulator must be changed.
Further control you can do is the recharge current, Toggle the cover on the lateral side where is the fuse holder, toggle the 30A fuse and put the terminal of Amperometr tester, start the engine and control the current, it has various values from 5A at minimum rpm at over 15A at the maximum rpm

Took battery had it checked, marginal at best, purchased new battery, installed and tested voltage at terminals, no change from yesterday.

Idle 9.8 volts dc
3000+ rpm 11.2

So I am thinking charging system. Am I on the correct track.

Yep, it's something in the charging system. The connector that joins the output from the stator to the voltage regulator may be corroded............or you may have a bad stator. The connector from the stator to the VR is under the right hand plastic panel. It takes a lot of disassembling to get to it but you'd also have to do this to change the VR so just in case the VR is totally shorted out and IT is the problem, you'll be in the right place to unplug the VR and replace it with a new one.

YES you on right track charging circuit, i would suspect its voltage regulator thats faulty

Usually (but not always), when the VR goes bad on these scooters, you'll get high readings rather than low ones........but, it's entirely possible that the VR is shorted out and simply not passing any current to the battery.

Other Piaggio products use the same VR as the BV500. Here's a recent thread where someone has to replace their VR on a GTS (exact same VR) Engine light on 09 GTS250 (Post 1501970)

Roninracer came into the thread near the end and you will see some links in one of his posts to the correct part number and where he bought his replacement VR. It's a Ducati part number. Good luck with getting the problem solved quickly and as inexpensively as possible.

Did you give it a full forming charge first? I'd be checking my multimeter if you did charge it properly first, otherwise all bets are off.

Il you want to check the stator voltage it makes a three phase voltage, you can check that where is a connector with three yellow wires, inside lateral cover, if you have an amperometric clamp, insert the clamp to the yellow wires and control the current flow, it must be 5-20A maximum. Check the electric insulation of the three wire with the rest of metallic frame.