Let me break it down from a language point of view so we can better understand how these words were chosen in the context of controlling the sound of musical instruments and thereby gain a better understanding of what they mean when used in a musical context.
The word brilliant describes a high degree of intensity in perception by the senses. Possible synonyms include sharp, vivid, intense, bright, radiant. The term brilliance is often used to describe the intensity and sharpness of light refraction on a cut diamond. The opposite of brilliant would be dull. A dull knife would not cut through things as well as a sharp knife.
In describing the sound of music, brilliance refers to how the sound is perceived by the ears. How sharp is the contrast between notes? What is the intensity level? Most likely on the piano you refer to, a higher degree of brilliance will equate to more treble and a more articulate sound with sharp contrast and high definition between the notes. More brilliance would mean a sharper cutting biting sound versus a warm and fuzzy mellow sound.
The word ambiance refers to a mood invoked by a place and what is happening at that place. It is the "atmosphere" or mood invoked by a certain place or environment in a certain situation. A crowded fast food restaurant with bright lighting will have a different ambiance than a quiet restaurant featuring private high back booths and candle lit tables.
In music "ambiance" is a term intended to differentiate how the music would sound in different environments or places. One way to portray the effect of particular places is through effects such as reverb (reverberation) or echo. Different places (venues) have different acoustic properties. Music played in a stadium would would be perceived differently than music played in an intimate small auditorium. Thus there would be a difference in ambiance. A big part of the difference sonically (which is the only part your instrument's controls can affect) would be the levels, amount and timing of the sound reverberation as the sound bounced off surfaces at varying distances and shapes.
So on the piano you refer to, "ambiance" likely will refer to the amount and type of reverb applied to the sound of the music as you play.
The word present means to be "here" and able to make your "presence" known by being seen or heard. The word "presence" was first used on guitar amps to describe a process whereby the treble frequencies were allowed to be more prominent or present (more there) by electronically cancelling some of the interfering frequencies. The "presence" control on many of the early guitar amps altered the sound by changing the dynamics between competing frequencies more than by boosting the treble frequencies as a treble control does. Today however, "presence" is often associated with the amount of treble.
But in terms of an effect - "presence" would be a way to define how much of the effect is "present" or "there". More "presence" on an effect would make it more obvious that it's there (or present).
For more on the presence control on guitar amps - see this question on Stack Exchange What does the presence control on my amp do?
Once you get your piano, you will want to play around with the effects and controls to see how they affect the sound and what you like and what works in various situations. Each brand keyboard or piano will use different means of altering the sound output via the controls - regardless of what they call them.
I would spend time playing with the various controls and settings in each instrument voice and make notes. Ultimately I would make a cheat sheet to remind me which settings and effects work best for each sound I plan to use and in each scenario I plan to use those settings and controls and effects in. The cheat sheet would include the levels or degree and type of "ambiance" I might want to use in various situations as well as exactly where to set the "brilliance" control for each voice or type music or even particular song.
I hope your new digital piano provides countless hours of entertainment and enjoyment.