What's the most common language shared by those who don't speak Common?

Question

Finding the most common language is easy¹, the number is written at the top of the Monsters section.

Finding the second most common² is also not hard, you just click through the list of languages, and note the second highest number. However, it is not necessarily the second most useful. That would be the most common language spoken by those who do not speak Common.

What is that language? Finding it might be a huge amount of manual work, clicking through for every monster, and collecting the languages, but is there a clever search pattern I can use?

(I am aware that the most useful language is largely campaign and level dependent.)

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¹ unsurprisingly, it is Common
² it is Draconic

Answer 1

Aklo, followed by Draconic and Undercommon

Searching

I searched for language:(-common aklo) ((-tongues -truespeech) OR Neothelid OR "Children Of Mhar") filtering for creatures (which includes both Monsters and NPCs), and I repeated this for each language.

The language:(-common DESIRED_LANGUAGE) part of the query is self explanatory, while the ((-tongues -truespeech) OR Neothelid OR "Children Of Mhar") part seems arbitrary, but is necessary for accurate results.
Tongues (as a constant spell) and truespeech are both effects that allow the creature to speak to anyone, so we need to exclude them from our results for the same reasons we want to exclude creatures that can speak Common. Unfortunately, even though tongues and truespeech are listed with the languages within statblocks, searching for language:(-tongues -truespeech) doesn't work.
Searching for -tongues -truespeech instead will erroneously exclude creatures that just happen to use those words in other parts of their statblock or even in their description. I did a second pass and found that (at the time of writing) only the Noethelid and the Children Of Mhar would be erroneously excluded, so to prevent this I added their names directly into the query.

Results

Language	No Common	No Common, tongues, or truespeech
Aklo	98	95
Draconic	102	81
Undercommon	79	78
Abyssal	77	65
Celestial	80	46
Sylvan	46	45
Infernal	62	33
Aquan	29	28
Necril	25	24‡
Mwangi	24	24
Tien	22	21
Terran	21	21
Jotun	18	18
Auran	16	16
Requian	20	15
Daemonic	14	14
Elven	14	14
Ignan	12	12
Akitonian	10	8
Protean	11	6
Alghollthu, Arcadian, Arboreal, Azlanti, Boggard, Caligni, Cyclops, Destrachan, Druidic, Dwarven, D'Ziriak, Erutaki, Formian, Goblin, Gnoll, Gnomish, Grioth, Hallit, Hwan, Ikeshti, Iruxi, Jistkan, Jyoti, Minatan, Munavri, Nagaji, Okaiyan, Orcish, Osiriani, Samsaran, Sasquatch, Senzar, Shadowtongue, Shobhad, Sphinx, Tengu, Utopian, Varisian, Vudrani, Wayang, Wyrwood	Single digits	Didn't bother checking
Adlet, Amurrun, Anadi, Androffan, Anugobu, Calda†, Ekujae†, Garundi†, Girtablilu, Goloma†, Grippli, Halfling, Jistka†, Kelish, Kibwani†, Kitsune, Kovintal, Lirgeni†, Mi-go, Mzunu, Ocotan†, Rasu†, Shae, Shisk†, Shoanti, Shoony, Skald, Strix, Thassilonian, Vanara, Varki†, Vishkanyan, Xanmba, Yithian, Ysoki	None	None
At least one language	474	432

† No creatures speak these languages, interesting.
‡ 4 of these creatures could know Common from their past life, and another 2 could know ancient Common, so depending on the DM, Necril creatures can go as low as 20 or 18.

Caveats

Obviously, these numbers are not representative of the actual languages and creatures you'll encounter in any given campaign. For example, your campaign's themes and setting might favor some languages over others. Moreover, you're likely to encounter several individuals who are the same creature, yet here they are counted only once.

Answer 2

This would depend on your setting

Each world has different monsters and different numbers of them. There cannot really be a generic answer to this. For what it's worth, my bet would be on Undercommon if your world has an Underdark -- it's like a second world below the world.

This is also supported by monster count for the languages - Halfling is listed as a common language, but only 6 monster types speak it, while Abyssal is listed as an uncommon language, but 134 monster types speak it. So counting by monster type, even by the game rules, does not determine how common a language is.

Monster Count: Draconic is the best common choice

I did a little counting: there are 747 monsters that speak common, 238 that speak draconic, 188 that speak sylvan, and 131 that speak undercommon. The other common languages are much less represented -- Jotun 90, Elven 57, Dwarven 27, Gnome 19, Goblin 15, Orcish 9, Halfling 6. I then did count how many of those did also speak common, for those that have enough monsters to have a chance to win. Out of curiosity, I also looked at Abyssal, even though that is an uncommon language, and so I would exclude it from running.

Language	Overall	Common	No Common	%Common
Draconic	238	137	101	58%
Sylvan	188	142	46	76%
Undercommon	131	52	79	40%
Jotun	90	73	17	81%
Abyssal	134	58	76	43%

Draconic wins. Draconic is so high as many fiends that do not speak Common also speak it, as the language of magic, I guess. Abyssal is closely trailing Undercommon. Dragons proper funnily enough nearly all speak Common.

So, I was ready to bet you 100 Rep it is going to be Undercommon, and I would have bet wrong. Draconic is the best option by absolute count and also by your measure with 101 monsters that speak it, but no common, followed then by Undercommon with 79, as the second best option.