Is there a specification for the "BEGIN RSA PRIVATE KEY" format? Until now I didn't find a specification (RFC or similar) for the file format that uses the BEGIN RSA PRIVATE KEY prefix and END RSA PRIVATE KEY suffix. Where is it defined? Is there an official name for it? It seems to be at least related to the series of PEM RFCs. 

I am looking for reference information about the details of whitespace handling, 
base64 details, joining of different keys in one file etc..

This question is NOT about the ASN encoding of the payload.
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.