What you said about giving gifts... My sister is a stage performer and when she was growing up, she had a mentor who was definitely a 2w3, and my sister told me about how she would do something similar; she would not ask for any gifts, but would be severely disappointed if she put on a play and she got no jewelry from the actors afterward. Honestly, though, she seemed to embody an unhealthy 2 to me; she had been an awkward adolescent, and she grew up not only to work with adolescents but to project her past wounds, insecurities onto them and turn them into projects... She wound up monitoring my sister's diet, clothing, behavior especially in regards to boys, and she came across saccharine and expected a lot of attention and gifts in return, without saying so directly. Other 2s I have been acquainted with (haven't gotten to know any extremely well, I have to say), though, haven't been that way... They felt very genuinely unselfish and giving to me. They seem to need more closeness than I ever could, though, but 2s are generally extroverts after all.
I have struggled with a strong line to 2 myself (eg, the less confident and the more desperate I have gotten, the more codependent, saccharine, needy, etc I have tended to become), and when I have come across unhealthy 2s like my sister's mentor I notice I have been unusually, extremely put off and have had difficulty sympathizing... I think I might be projecting my own dark side onto them.