...I think early 230 SLs have the float-type sender (looks like a conventional gas float on an arm, etc)...
That is correct.
The early style float and lever type sender was used up to chassis number 008953 for all LHD 230SL's and up to chassis number 013302 for all RHD 230SL's.
Sadly this part has been NLA from Mercedes for quite some time.
There is an upside however, the same type of sender was also used in the early fintails (220Seb, 230S and 220SE coup/conv.).
...If you have an early 230 SL and someone replaced the early float sender with the late tube sender, this could explain what you are experiencing...
Also correct as the gauge in the in the instrument cluster is different for the early and late style fuel sender units. You cannot used the later style sender with an earlier gauge as your readings will be different.
The reserve warning light has a delay built into the circuit. Once contact is made, the light would come on after a few minutes. This is to avoid the light flickering due to contact bounce whilst driving with a tank close to the reserve mark.
The lag is typically 4 to 7 minutes.
All pagodas after the above mentioned chassis numbers should have the later tubular style sender unit. If so, then you have nothing to loose by removing it from the tank and open it up for an inspection and clean.
The usual precautions apply when working with gasoline and always replace the fuel sender gasket on the tank.