actually you are trying to download the dl extract for an old license, however you have to follow different for which i have tried to give steps, hope you will be able to follow:
on this website https://parivahan.gov.in/sarathiservice
select gujrat
then go to
apply online
>Services on driving license
>Click continue
>Enter dl no and dob and click Go, this will pull your RTO details online
>select submit request to> State> and RTO> Click Proceed
on next page it will show you your photo and all details, On subsequent pages it will give you option to apply for DL extract online, saarthi webste will give option to book appointment online if the option is available in your rto. at the end you will be able to download a prefilled pdf form and acknowledgement , you simply have to take the prefilled form to your rto and apply for dl extract.
this is the process to apply for DL extract on esaarthi website. hope i could explain in whatever little time i had.
I entered my DOB and DL and clicked GO. But it pulled nothing from RTO data.