Vendor trying to Rescind.

State: NSW
Property: Residential house and land.

Day after cooling off, vendor tells their solicitor they no longer want to proceed with going ahead with the sale. Reason: 'Allegedly didn't know what they were signing'
Real reason: Agent told us they were trying to purchase another property and it's alleged to have fallen through.

Vendor's solicitor advises Vendor does not want to proceed due to them allegedly not knowing what they were getting in to or signing.

We are not accepting of the rescission at that time, vendor allows mortgage company directed valuation to proceed.

Now today we receive letter from solicitor advising the vendor will be rescinding due to mental illness.

Wow, this is pretty damn out of the ordinary.

Anyone had experience in this area?

What's chances of us winning civil action here with a notice to complete?
Anyone recommend a GOOD solicitor who has had experience in this?
Get yourself a solicitor of your own.

Sounds like the vendor's solicitor is coaching them. I'm sure one of the solicitors on this forum can give a lot more information but from what I understand if you enter a contract with a diminished mental capacity or being not of sound mind it makes the contract voidable.
Write to the other side's solicitor and ask for evidence of the mental illness, what is the diagnosis, who made the diagnosis and when was it made. Tell them you will be asking that they go and see a doctor of your choice and what days and times will they be available.

If they fight this are you prepared to fight back?? They have the upper hand at this stage, and know if will be easier for you to pull out rather than fight. If you decide to pull out you want to make sure you don't let them out easy.
Reminds me of a client. The parent had early stage dementia and engaged a RE agent who promptly sold the house. Seems agent introduced Dad to a local lawyer to do the sale contact. Then listed it then sold it in a few days. Daughter horrified a few days later when some paperwork arrived in mail - By which time Dad was confused and couldn't understand why his house was sold. Daughter engaged a lawyer. Other party wasn't happy but accepted the issue. The Dad had given POA to daughter for that reason and lacked capacity to even engage the agent who didn't note any issues.

It does happen.
On the other side there could be a number of reasons why the vendor isn't able to purchase a new home. They might be in a position where they can't get reasonable finance at all (a really nasty default or two).

They want to buy another house but simply can't and are now facing not owning a home at all.

It's not right that they want to pull out of a legally binding contract but I do find that most people selling do genuinely want or intend to sell.