Visiting India - Entry or Tourist Visa?

[klal]

Here's my situation - both my wife and I are PIO Card holders and therefore do not need visas to visit India. My son, born Indian and now a UK citizen surrendered his Indian passport recently. He will obviously need a visa to visit India. My daughter was born here after we had become British citizens which makes her (my daughter) a British citizen by birth. My question is - are both my children eligible for a tourist visa to visit India or will they need an "Entry Visa?" I ask because I've come across information which seems to suggest that Persons of Indian Origin and their children are NOT eligible for tourist visas and must apply for an Entry Visa! Can anybody confirm this is actually the case?

And finally, in the case of my son who has completed sixteen years of age, does he need to sign the visa application form himself or does it have to be a parent?

Grateful for any help and pointers.