"So I suppose that this sensor had already been assigned some light index different than 1." If you don't have any bike computers, watches, etc around this is most likely the result of some command you sent in error. Lights will not form a network unless they are commanded to do so, and will timeout if the controller does not maintain the network (see 5.2.4). Note: Some controllers may automatically pair to lights that are in close proximity without user interaction.
"5.6 of Lights Device Profile Rev 2.0_M.001 does not provides details about controlling lights via the broadcast channel": Section 5.6 just describes the process of pairing to the broadcast channel and sending whatever commands you wish. The details of each currently supported command page are in sections 7.16, 7.17, 7.18, and 7.19.
"I was just sending page 33 with light index 2 to light sensor. After that I tried sending page 34 with light index 0 and expected to see new beam mode, but it does not change": I have not been able to reproduce this behavior either. You may be encountering the condition where the network times out just after you send your page 34, causing your commanded changes to be overwritten. You should be able to see this by looking at the light index transmitted from the light as the light index going from 0 to 2 to 0. I almost hit this case in my testing. The light changed only momentarily to be on, and then turned back off.
"Ian, can you please elaborate what commands from controller does RTL expects while in pairing mode?
Is it enough to send single page34 request so that RTL pair with this controller?": A single page 32, or 33, or 34 (the pages with controller id) properly formatted such that the light accepts it while in pairing mode is sufficient. Check the light index for connect and disconnect command acceptance and see 5.4.1 for determining setting command acceptance.