Modern Vespa

Hi guys. I'm new to this forum so please be kind. I'm Steve from Cornwall UK and have just bought a Piaggio xevo 400ie in a private sale.
This is another "no master key" question and I have searched previous posts but haven't found anyone with the same symptoms as I have.
So, I didn't know about the master key thing and bought the bike with just one blue key. The bike was starting OK and I drove it home.
This is what is happening.
Came to the bike the following morning and noticed a coolant leak coming from the thermostat. Fortunately the guy I bought it off had given me a spare engine so replaced the leaking one with the one off the old engine.
Started it up to bleed the air out. Turned it off and then it wouldn't start again.
So, I switch ignition to on, hold brake lever, turn kill switch to run and the immobilizer light briefly goes off then pulses very fast so almost a solid light.
The bike cranks but won't start.
Here is the strange bit. Came to it the next morning and it starts straight away. Went for a quick ride and switched off at home, tried to start it again and same thing, very fast pulsing light, cranks but no starting.
It seems that if I leave it for a few hours it starts straight away but won't re start after that.
I am hoping that one of you experts can give me a clue as to what it might be and what I can do about it. I have already asked for my money back but the guy seems to think it might just be the antenna at fault.

Found some info here

Immobilizer LED codes

Manual here

https://www.manualslib.com/manual/1111452/Piaggio-2005-Xevo-400ie.html?page=52#manual

Just guessing here but assuming the seller claims it was OK previously and it seemed OK when you got it has anything changed? Did you need to disturb any wiring doing the thermostat or is the key now on a big bunch of other keys (apparently this can make a difference).

Worst case it seems like you can disable the immobiliser fairly cheaply.
Quick search also found this

https://www.gtmotoparts.com/products/replacement-keys-immobilizer-removal-bypass-for-piaggio-x9-beverly-500cc-nexus-500-iaw15p

Your local Piaggio/Vespa dealers can get you a brown key. check that your brake switches and brake lights are working some bikes use the light to complete the circuit. i think the coolant level is not the issue.

Thanks Gf350. I might need to get one of those "no immobilizer" things but I guess I have a few things to try first.

Don't think I disturbed anything and just a single key.

I contacted a company called Motomatrix who wrote ....

"my guess would be the initial power going to the key reader is insufficient to read the key , can be ecu or key reader or amplifier .. later on when ecu is cooler it sends good strong power on start up .. try removing wires going to the ecu for 5 minutes and then connect and see if it starts .. if it starts when power is introduced again then this is the problem .
P.S. Thanks for the links.