We don't even know where basque-speakers were during good part of the iron age, not to mention bronce age. Their presence in Spain is first attested by a few roman era scarce anthroponyms.
In my opinion this argument does not hold up, since you might as well argue the same about the Celtic-speaking peoples of Iberia: we do not have any evidence for Celtic languages in Iberia before the Roman era*, because nothing was written down. Yet we normally assume they were already there.
*it should be elaborated that the bulk of the Celtiberian written material, even in the Iberian script, comes from the Roman period (2nd century BC), too.
Mitxelena's studies on basque language support a dialectal unity in the Early Middle Ages, something really strange for a language wich has supposedly been spoken in Spain/France for several millenia. Neolithic basques? Maybe... but probably not in south-western Europe.
I agree that the Basque language area in Antiquity was more northern and eastern than it's present-day position, and that only the eastern part of the present-day Basque country was actually Basque in Antiquity. But, the premise that the Basques are not native to there, and only immigrated to the location we know in Antiquity opens a cans of worms of problems: are we to say that the Celts somehow are native where the Basques are not? For the Celtic languages, we find related languages (read: other Indo-European languages) as far east as the Indian subcontinent (Indic languages, attested first with Sanskrit) and the Tarim Basin (Tocharian). For Basque, we have no definite relationship with any other language, other than Aquitanian, which closely resembles what has been reconstructed for Proto-Basque. We do not know how long it takes for two languages no longer being recognizable as being related, but given how we have for example the Afro-Asiatic and Uralic language families (both which are clearly Neolithic in age), this certainly reinforces the idea that Basque is an ancient language.
It should also be added that it is sensible to assume that the Basques had no contact with speakers of Indo-European languages until the bronze age, or possibly even the iron age (note that Basque has a native word for iron, but it's just as possible that the word originally just meant generalized "metal", and not explicitly "iron"), due to the fact that there is only a tiny number of Celtic loanwords into Basque.
With some words about horses and charriots occurs the same that with metal-working terms. If there are "patronimical" words in both cases, we should at least valorate the possibility that have been "generated" by analogue processes.
In northern Spain, bronce metallurgy and charriots are first attested in second half of II millenium.
What is unclear is the connection of Basque with the Iberian language, which after all was spoken across a wide arc from the Roussillon to eastern Andalusia. What is agreed upon is that there appears to be a common pool of shared vocabulary, either through language contact (Basque loanwords into Iberian, or vice versa), or because the two languages belong to the same family. The former appears to be more likely, due to the fact that Basque has been of little help in the decipherment of Iberian. In any case, the Iberians were (seemingly) autochtonous on the Iberian peninsula.
I have to ask however, what exactly do you mean by "patronymic" words?