280 Watts sounds like its on the low side for a sliding gate opener, must be a fairly light weight gate? We don't know what kind of motor it is to estimate start up surge. An AC induction motor will have a MUCH larger surge than an electronically controlled DC motor like is found in some garage doors.
If the gate takes 1 minute to open and close (30 sec each way) and you use it 20 times per day. That is only 280W x 0.33Hrs = 92.4Wh
Lets round off to 100Wh per day. Your 20W, 12V solar panel would be expected to produce about 100Wh per day on average but less on cloudy days so I would say its marginal at best and probably undersized but may work for an initial set up.
If your inverter can pull 49A at 12V then it sounds like a 500W model. However, if your gate opener only needs 280W then the Inverter only uses the amount of power it actually needs. 280W/12V = 23.3A (actually a little more due to inefficiencies) BUT this does not take into account the potential surge current necessary when a motor starts up. Here again a 500W Inverter is marginal in the best case and way undersized if we are talking about an AC induction motor that has surge of 5x the operating current. I would recommend a minimum of a 1,000 Watt Inverter. Before proceeding we must have more specifics about the gate opener motor type and what is referred to as LRA. Locked Rotor Amps.
If you have 2 x 12V batteries they probably have sufficient Amp Hour capacity to open and close the gate several times and store the necessary solar energy. Are they rated for the peak Amperage Surge which we don't know at this point.
Sorry, we have not answered your question in entirety. I hope it gives you some clarity and identifies what the next steps are.
