Ships are supposed to actively cooperate with a system called AIS (which is like aviation's ADS-B).
https://en.wikipedia.org/wiki/Automatic_identification_syste...
If they use AIS as required, they will be identified by receivers that they pass nearby.
Process of elimination. List of all known ships (tankers). Rule out ships accounted for (alibis). Investigate the handful of rouges.
turning off radios would prevent inadvertent/automatic transmissions
disabling transponders would reduce footprint on more modernized port control radars
not using radar from ownship reduces the chance of being seen
all these together would render the ship's ELINT footprint down to an old school blob on whatever radar plot
that's about as anonymous as you can get without active countermeasures and those are VERY obvious
Anyone can make a jammer, but it only helps if you can evade your pursuer before they get a look at you optically; it's not much use for a lumbering oil tanker.
As zentiggr says, you can get some degree of passive stealth just by turning off your own radio/radar, but anything more than that requires a custom-engineered (and strangely-shaped) hull, propulsion, etc. that takes military-level money to design and would be extremely obvious in any port. So, again, not practical for this kind of smuggler.
https://g1.globo.com/economia/noticia/2019/10/25/petrobras-d...
https://www.marinha.mil.br/manchasdeoleo/informacoes-sobre-o...
http://www.petrobras.com.br/fatos-e-dados/recolhemos-mais-de...