Can RSA signing be implemented on top of RSA encryption/decryption?
Yes, you can, but you would need access to raw or textbook RSA encryption and you would have to implement the PKCS#1 v1.5 or PSS padding primitives yourself. Beware that PKCS#1 v1.5 compatible padding is different for encryption signature generation.

If you only have PKCS#1 v1.5 encryption or OAEP encryption available then the encryption routine will already pad your data, and in that case you cannot use the encryption API to sign.

The padding methods in common use are found in RFC 3447 which basically is a copy of RSA/EMC's PKCS#1 v2.1 specification.