We need to capture the Signature Status in order to identify whether PDF file was actually signed or not.
I have incorporated the changes using following script and attached the modified PDF for your reference.
var signStatus1 = this.getField("Signature1").signatureInfo().status;
if(signStatus1 != 0)
{
this.getField("Signature2").display = display.visible;
}
The overall logic remains the same, initially keep the Signture 2 and 3 fields hidden and then enable it via script.