Is there a specification for the "BEGIN RSA PRIVATE KEY" format?
I'm here, because, I'm asking myself the same question as the OP.

PKCS#1 (RFC 3447) defines the ASN.1 structure: RSAPrivateKey, permitting the
expression of an RSA private key only.

PKCS#8 (RFC 5208) defines the ASN.1 structure: PrivateKeyInfo, permitting the
expression of any private key. (For an RSA private key, PrivateKeyInfo is some
packaging information, and a reuse of RSAPrivateKey from PKCS#1).

PEM (Privacy Enhanced Mail), is a defunct method for secure email. But, its
container format was borrowed for packaging cryptographic items.

RFC 7468 (Introduction): "For reasons that basically boil down to non-coordination or inattention, many
PKIX, PKCS, and CMS libraries implement a textbased encoding that is similar to
-- but not identical with -- PEM encoding."

Which reads as: Um, folk have decided to use bits of PEM to package thier
crypto files. Here we have a jolly good effort to try and formalise that... 

Alas, RFC 7468 clarifies the PKCS#8/PrivateKeyInfo packaging as "BEGIN PRIVATE
KEY". But not the packaging of PKCS#1/RSAPrivateKey as "BEGIN RSA
PRIVATE KEY".

The "BEGIN RSA PRIVATE KEY" packaging is sometimes called: "SSLeay format" or
"traditional format" for private key. Which, as least, gives us a name for this
format, but, like yourself, I cannot find, and would welcome, something that
approaches a formal description of this format. I suspect this does not exist.